FORTUNE — Anyone care to run an $54 billion-a-year tech giant? Anyone have any good ideas how to get it growing again? Intel is looking for a new CEO to take the reins at the Silicon Valley icon next May, when Paul Otellini steps down from the job.

Since Otellini became CEO in May 2005, the stock has lost 22% of its value, against a 52% gain for a recession-challenged Nasdaq. Much of Intel’s (INTC) decline has to do with secular changes in the market for processors as mobile devices have eaten into demand for PCs. Otellini’s legacy is seen as strong on engineering advances but not so strong on anticipating the broad changes seen in the tech world over the past decade.

For a while, Otellini looked to be managing Intel’s growth well enough. After Intel’s stock bottomed out at $12 a share in the recession of 2009, it rebounded to $29 a share six months ago. Since then, the toll that the tablet economy is having on the longtime WinTel PC monopoly has become more evident, and the stock has fallen back below $20 a share.

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Intel has gone from dominating the chips made in personal computers running Windows software to being threatened by ARM design chips, which dominate mobile devices. It’s producing chips based on the x86 architecture for smartphones and tablets. But these aren’t selling anywhere nearly as well as ARM-based devices, and investors are starting to be concerned that time is running out.

So Otellini’s successor will face some daunting challenges. Analysts are expecting revenue to decline in 2012 for the first time since 2009 and earnings to fall by 12% to $2.11 a share. In 2013, they’re expected to fall further — to $1.95 a share. There are a few things, however, that Intel can do to get its financials growing again. Here are some possibilities:

N0. 1 Keep Apple happy. Switching to a new chip architecture is a big and risky decision for a computer maker, but Apple (AAPL) moved to Intel processors for its desktops and laptops in 2005. But it’s going to happen again if Mac OS X merges with iOS, which seems all but inevitable at this point.

Recent rumors suggest Apple could move to ARM processors in its Mac computers, although that could take years. But the reverse could also happen. RBC analyst Doug Freedman wrote in a research note last week that Apple, as it moves from Samsung as a foundry, could opt for Intel’s x86 chips in its next generation iPad.

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No. 2 Build a better hybrid chip.Not only is Apple likely to merge its mobile and desktop operating software, Microsoft (MSFT) is already making similar moves with Windows 8. If the lines between older and newer computers continues to blur, Intel has a chance at becoming the standard. As the company likes to point out, it can design and manufacture the chip, ensuring a smoother end-to-end process — a claim that not all chipmakers can make.

No. 3 Push deeper into data centers. While Intel’s PC Client division makes up two-thirds of revenue and the Data Center group makes up only a fifth, it’s the latter where profit growth is coming. The Data Center unit, which includes server platforms, is seeing revenue grow at 7% a year and operating profit margin of 47%. Compare that with the 2% revenue decline and 40% profit margin of the PC group.

This is an area where Intel can keep growing even if global demand remains soft. The company says it’s facing competition from big names like IBM (IBM) and Oracle (ORCL), but its brand can carry some weight. Strategic acquisitions could speed this up, which may be helpful. Some ARM chipmakers are moving into the server market as well.

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N0. 4 If all else fails, pay off investors. Under Otellini’s tenure, Intel has paid out $24 billion in dividends. It’s put more than $46 billion toward stock buybacks since 2005. That’s an average of $8.8 billion a year is cash straight to shareholders. (By contrast, Intel spent $8.4 billion on R&D last year.)

On Tuesday, Intel said it was taking advantage of its A+ credit rating to offer $6 billion in new debt, much of going toward more stock buybacks. It could be Otellini’s parting gift for Intel’s next CEO. If the company doesn’t meet the challenges facing it, that cash could come in handy.