* Obama team to work on stimulus, financial rescue plan
* Fiat takes 35 percent stake in Chrysler
* France plans $7.8 bln auto aid
* Bank shares drop; European, U.S. stocks fall 2 pct
* German ZEW index higher than expected but job cuts mount
By Daniel Trotta
NEW YORK, Jan 20 (Reuters) - Barack Obama took office on Tuesday amid a deep economic downturn, a trillion-dollar federal deficit and a gasping bank sector, and the first African-American to become U.S. president vowed to meet the challenges.
His aides promised to go to work immediately, armed with the authority to spend the second half of the $700 billion financial rescue plan and a proposed stimulus package of $550 billion in spending and $275 billion in tax cuts.
Stock prices extended losses while Obama spoke as investors were disappointed they did not hear more specifics regarding his promises for bold and swift action.
"People were looking for something, new plans, new hopes," said Joe Saluzzi, co-manager of trading at Themis Trading in Chatam, New Jersey. "They didn't hear something new."
Obama said the country understood it was in the midst of crisis, mentioning war, a sagging confidence and an economy that was "badly weakened, a consequence of greed and irresponsibility on the part of some."
"Today I say to you that the challenges we face are real. They are serious and they are many. They will not be met easily or in a short span of time. But know this, America -- they will be met," he said upon taking the oath.
Obama also hinted at greater regulation, saying "this crisis has reminded us that without a watchful eye, the market can spin out of control."
The new president was riding a wave: A CBS News/New York Times poll showed 79 percent of Americans are optimistic about the next four years.
But that did not help the Dow, which was down more than 2 percent in early afternoon trade, extending the 2009 slump to nearly 8 percent.
Shares in major U.S. banks were down double digits after State Street Corp, the world's biggest institutional asset manager, reported billions of dollars of unrealized losses in its commercial paper program and investment portfolio.
State Street stock plummeted 50 percent while Citigroup, Bank of America, JPMorgan Chase & Co and and Wells Fargo were all battered.
"It's very uplifting (Obama's inauguration) but I'm not sure it's sufficient. I don't really see this influencing medium-term investment decisions," said Marc Chandler, head of global currency strategy at Brown Brothers Harriman.
"There still is a danger that we are doing too little rather than too much," he said in reference to the stimulus and financial rescue plans.
POUND GETS POUNDED
Europe's banking index fell to a 14-year low on fears that lenders will need more state help to raise capital. Shares of Lloyds dropped 31 percent and Barclays fell 17 percent.
On Monday, Britain threw its troubled banks a second multibillion-pound lifeline in three months and gave its central bank approval to pump cash into the ailing economy because interest rates were close to zero.
Concerns about the British banking sector pushed the British pound below $1.39 for the first time since June 2001.
European shares fell 2 percent despite a better-than-expected ZEW analyst and investor sentiment index report in Germany. The monthly poll of economic sentiment by the ZEW economic think tank rose to -31.0 from -45.2 in December.
"This is mostly an expression of hope. The (ZEW) indicator is still clearly in negative territory. Nothing is changing in terms of the 2009 recession," said Gerd Hassel, an economist at BHF-Bank.
The Bank of Canada cut its benchmark interest rate 50 basis points to a 50-year low of 1 percent, the latest effort by the world's leading economies to combat recession.
Japan reported consumer confidence plunging to a record low last month in yet another sign of deepening recession.
CAR CRISIS
Except for banking, no sector has been harder hit than carmakers by the financial crisis, the worst in 80 years.
Italy's Fiat took a 35 percent stake in Chrysler, launching a venture designed to secure the beleaguered U.S. carmaker's future.
The deal aims to give the Italian carmaker the scale it needs to survive and let Chrysler expand its product portfolio to include small, less-polluting cars.
Separately, France said it may pump up to 6 billion euros ($7.8 billion) into the country's ailing car industry. Prime Minister Francois Fillon warned that automakers would have to safeguard jobs in return.
"There is an emergency. We need a massive response on the automobile sector's financing," Fillon said.
German Chancellor Angela Merkel, however, said the aid threatened to distort competition and was not a long-term solution to the struggling sector's problems.
EU Industry Commissioner Guenter Veheugen said the EU must watch efforts to rescue U.S. carmakers to ensure they do not disadvantage European manufacturers. (Reporting by Reuters bureaus worldwide; Editing by Brian Moss and Steve Orlofsky)