Anger is mounting in Cork. The vexing issue of tax – specifically, how much the Irish government should be collecting – dominates the city.

Placards strung from lampposts indicate widespread disquiet; the airwaves are dominated by splenetic voices proclaiming that there is one law for the rich and another for the poor; a meeting on Monday in the city's Metropole hotel will hear proposals for a mass protest, with leading politicians calling for Ireland's citizens to stop paying their taxes. Across the city, the controversy surrounding the introduction of new water charges, to pay for improvements to Ireland's crumbling piping systems, is impossible to ignore.

Perhaps the new water charges would be unnecessary if the Irish government had levied higher tax bills on one of the country's largest and most prestigious employers, technology giant Apple – not to mention the other IT and big pharma companies that have chosen to base themselves in the country.

For years, the government has lured foreign blue-chip firms to Ireland with a 12.5% corporation tax rate, the second-lowest in Europe, and the strategy has been hugely successful.

According to the American Chamber of Commerce, the body that represents US business interests in Ireland, more than 115,000 people are directly employed in over 700 US firms in the country, which collectively contribute some €3bn (£2.35bn) a year to the Irish exchequer and have invested a staggering $190bn (£118bn at current rates) in its economy.

And Apple is the jewel in the crown, the symbiosis between the country and the corporation exemplified in the decision by U2 to give their new album, Songs of Innocence, away for free on iTunes.

Nowhere in Ireland is Apple's presence felt more keenly than in Cork. High above the city, opposite a travellers' site and a field of tired-looking horses, is Apple's European HQ. At the end of Tadhg Barry Road, named after a prominent trade unionist, it is a paean to modernity that squats in stark contrast to the vacant 6,000 sq ft warehouse now up for sale next door.

The Apple Campus, as it is known locally, does not so much look built as beamed down from the future. View the headquarters from the back, through a sturdy metal fence and across a field of artfully cultivated wild flowers, and it becomes apparent how much the campus owes to the Californian company's obsession with design. Green glass and sleek grey panelling are heavily favoured. The buildings, monitored by countless CCTV cameras, resemble giant iPods.

Apple's importance to Cork is such that in 2012 the city council took the extraordinary decision to expand its boundary so that land adjacent to the campus could be given over for a giant car park to facilitate Apple's expansion plans. Apple almost pulled out of the city a couple of decades ago, but now employs more than 4,000 people (compared with just 60 in 1980), making it Cork's largest private-sector employer. The company recently completed a €300m extension on its campus and has leased more buildings in the city centre, including several apartments in Ireland's tallest structure, the Elysian Tower, near Cork's waterfront, so that it can provide its top executives with luxury accommodation when they visit the campus.

Take the 202 bus from outside Apple's Knocknaheeny HQ back into town and the corporation's impact on the city becomes apparent in another way. Except for the driver, almost everyone on board is from outside Ireland. German, French, Italian and several eastern European accents compete for attention. With ID cards strung proudly around their necks, the employees, mostly in their 20s and wearing trainers and smart jeans, constantly check their iPhones as they exchange small talk with their colleagues.

Down the hill leading back into the city, Aidan Winnett, 21, is waiting for a friend to pick him up. He laughs when asked about Apple's presence in Cork. "I'm not a fan; they're just so up themselves, you know?" But what of the thousands of jobs that Apple has created? He shakes his head. "All for foreigners."

This, Apple's many supporters in the city maintain, is a myth. "More than 60% of Apple's employees are Irish," said Conor Healy, CEO of Cork Chamber of Commerce. "Apple's been in Cork for more than 30 years and it's been good for the city not just in terms of jobs or financial returns but its reputation, too."

Apple's presence, it seems, has helped put Cork on the map and suck in other hi-tech firms, creating something of a virtuous circle. In addition, Apple's presence in Cork is estimated to have generated 2,500 further jobs.

"The fact that we can attract highly skilled people to Cork is a good thing," Healy says. "It's a vote of confidence in the region."

But the virtuous circle is now threatened on two fronts: by the European commission's announcement that it is to carry out a detailed investigation into two tax rulings relating to Apple issued by Ireland in 1991 and 2007, and an ongoing US Senate inquiry that has claimed that the tech giant is paying as little as 2% in corporation tax on its non-US activities.

How both inquiries are resolved will say much about where power lies in a globalised world. Does it still reside with nation states or with giant corporations?

The inquiries' outcomes will also resolve the tug of war between the US and the commission. American politicians accuse Apple of deliberately shifting profits to Ireland to minimise its US tax bill. The commission's case against Apple is that it is not paying enough tax in Ireland.

Both the Irish government and Apple deny the claim that the company has had favourable treatment.

"Apple has received no selective treatment from Irish officials over the years," the company said in a statement. "We're subject to the same tax laws as the countless other companies who do business in Ireland. Since the iPhone launched in 2007, our tax payments in Ireland and around the world have increased tenfold. To continue that growth – and the benefits it brings to the communities where we work and live – we believe that comprehensive corporate tax reform is badly needed."

That the commission and the US can take such different views about Apple's profits and tax liabilities is instructive. Any tension between those views exposes a fundamental flaw in an increasingly globalised world. Taxation systems drawn up in the 1920s are proving wholly inadequate for taxing a sprawling multinational behemoth such as Apple, which manufactures its products mainly in China but derives the majority of its profits from its intellectual property – its branding, marketing and patents – which are funnelled through a complex maze of companies, including two in Ireland.

"We've moved from relatively simple operations, where companies made things and sold them, to a fragmentation of the supply chain, where intellectual properties, intangible assets, are becoming more important," said Heather Self, a tax partner at law firm Pinsent Masons.

Apple is far from alone in claiming that profits from large chunks of its intellectual property are generated outside the US. A significant portion of Microsoft's intellectual property is located in exotic offshore locations. Google declares profits in Bermuda, where corporation tax is zero.

However, Apple seems to have captured the imagination of legislators on both sides of the Atlantic. Self points out that the taxation strategies of Caterpillar, the earth-moving company, have already been subject to similarly forensic scrutiny from the Senate committee. "But it has received far less traction than Apple. It's because it is a consumer brand that Apple is getting so much attention."

Seamus Coffey, a lecturer who has taught economics at University College Cork for the past 13 years, has followed Apple's progress closely. "Apple is accused of declaring certain profits to be stateless," Coffey said. "They might be for tax purposes but in reality they have to be somewhere. The US Senate has basically accused the profits of being in Ireland but the counter to this is that the European commission has said the profits here are too low and Apple is not declaring enough profits."

As the transatlantic standoff continues, one thing is clear: Apple is sitting on huge sums of money – $137bn last year – much of it generated from its profits on intellectual property that the US government would like to tax.

The money is, according to reports, residing in a Manhattan bank, but legitimately classed as being held outside the US. Only if Apple were to "repatriate" the money would it be landed with a huge tax bill.

To some extent, Apple's tax problems are a result of its stellar growth, and that has made its tax arrangements far more interesting to legislators. "Apple was a completely different company and on the verge of bankruptcy in 1995," Coffey said. "It was only when Steve Jobs came back, and really only from 2007 and the launch of the iPhone, that profits started to lift. In some ways it is a victim of its size. It has become very visible. But there is no doubt that it has what most would consider to be a questionable tax arrangement."

Typically, corporation tax accounts for only 8% of a country's tax receipts and is dwarfed by its VAT and income tax receipts. Some in Ireland may take the pragmatic view that even if hi-tech companies like Apple are using legitimate but questionable structures to minimise their corporation tax demands, they will still be significant contributors to the exchequer.

"People are well aware that Ireland is attractive for these companies," Coffey said. "Given the number of jobs involved, they see the advantages of it. Cork is a mid-sized city. Some 200,000 people live in the city and 200,000 in the surrounding environment, so 4,000 jobs is massive. People are concerned about jobs, not tax practices."

But the US Senate and the European commission disagree. Some time soon Apple will have to decide whether it is in Europe or America. Ireland has wrestled with the same question for centuries.