* European shares rise 0.5 pct, MSCI world index up 0.15 pct

* Apple hit with $14.5 bln EU tax bill, say will appeal

* Dollar regains momentum, touches 2-1/2 week high

* Market starting to bet on December rate hike

* Commodities steady

By Marc Jones

LONDON, Aug 30 (Reuters) - U.S. interest rate rise expectations pushed the dollar up for a seventh time in eight days on Tuesday, while Wall Street dealers braced for a bruising session for Apple after it was hit by a record $14.5 billion European tax bill.

The dollar hovered at a 2 1/2-week high against other top currencies ahead of U.S. trading as the overarching theme of interest rate moves helped Europe's banking and industrial stocks push the FTSEurofirst 300 higher.

Doubts remain about when U.S. monetary policy will change, especially with an election in November. But both Fed Chair Janet Yellen and Vice Chair Stanley Fischer have suggested in recent days that the case for a rate increase is strengthening.

Fischer spoke again on Tuesday and repeated that U.S. employment is strong and that a "one and done" rate hike cycle is not something central banks like the Fed tend to engage in.

"The market is now pricing around a 36 percent probability of a hike in September and it has moved from about 50 to 60 for December, which is considerably higher than a week ago," said Rabobank's U.S.-focused economist, Philip Marey.

"Now we are waiting for the next big thing, which is payrolls (U.S. jobs data) on Friday," he added, saying the first batch of Q3 GDP data at the end of October would be key.

Early Wall Street trading was set to be dominated by Apple after EU antitrust regulators ordered it to pay up to 13 billion euros ($14.5 billion) in taxes plus interest to the Irish government after ruling a special scheme to route profits through Ireland amounted to illegal state aid.

Both Apple and Dublin said they would appeal the massive sum, which is 40 times bigger than the previous known demand by the European Commission to a company in such a case.

Online retailer Amazon.com Incand hamburger group McDonald's Corpface probes over taxes in Luxembourg, while coffee chain Starbucks Corp has been ordered to pay up to 30 million euros ($33 million) to the Dutch state.

"Nobody would dispute that corporations need to pay their fair share of tax, but a retroactive cash-grab creates uncertainty," said CMC Markets analyst Jasper Lawler.



BREXIT BRUISES

The focus on U.S. rates put bonds under pressure, with German Bund yields pulled up by 10-year Treasury's rise to 1.5850 percent.

The yield on Italy's 10-year BTP bond recovered after an early wobble as it sold 7.75 billion euros of debt at a record low cost despite uncertainty surrounding a referendum later in the year that Prime Minister Matteo Renzi has pinned his future on.

There was a fresh blow to hopes for Transatlantic Trade and Investment Partnership (TTIP) deal between the United States and Europe as France joined Germany in calling for an end to the negotiations.

Brexit bruises were also beginning to show.

Economic sentiment in the 19 countries sharing the euro fell in August to its lowest level since March, a further indication that morale is weakening after Britain's June 23 vote to leave the European Union.

Bank of England figures meanwhile showed that lending to consumers slowed last month urn:newsml:reuters.com:*:nL9N0MN001 and the Confederation of British Industry (CBI) warned investment plans among services firms, the largest sector of the British economy, were at their lowest in more than four years, urn:newsml:reuters.com:*:nL8N1BB191 .

"Looking ahead, the service sector faces a challenging environment in which to grow and invest, with uncertainty about demand weighing on firms' minds," said the CBI's head of economic analysis and surveys, Anna Leach.

The signs of weakness in the economy and the uncertain outlook for U.S. monetary policy led sterling to slip back towards $1.30. The pound has fallen more than 1 percent against the dollar GBP=D4 since Friday's comments by the Fed's Yellen and Fischer.

"The BoE's easing bias, softer UK economic data and sterling's role as a funding currency will all keep the bearish ... momentum in place," said ING currency strategist Viraj Patel.

In commodity markets, oil steadied after falling by around 1 percent on Monday. Oversupply remained a major concern, with U.S. crude stockpiles forecast to have risen by 1.3 million barrels last week, a Reuters poll showed.

Brent crude futures were up 29 cents at $49.55 a barrel, U.S. crude added 39 cents to $47.36, while gold slipped 0.2 percent at $1,320.79 per ounce.

In emerging markets, Brazil was in the spotlight. Senators are due to vote late on Tuesday or early Wednesday on whether to convict suspended President Dilma Rousseff and remove her from office over breaking budget laws.

If she is dismissed, interim President Michel Temer would officially take over as Brazil's leader to serve out the remainder of the presidential term through 2018.

Brazil's real BRL= , which has been one of the world's top performers this year, was up 0.2 percent at 3.2215 per dollar.

(Additional reporting by Wayne Cole in Sydney and Jemima Kelly in London; Editing by Catherine Evans) ((marc.jones@thomsonreuters.com; +44)(0)(207 542 9033; Reuters Messaging: marc.jones.thomsonreuters.com@reuters.net Twitter @marcjonesrtrs))