Doing business abroad can have consequences as enforcement continues to ramp up and new legislation gets enacted, yet most senior executives either don't know about it--or they don't think it applies to them.

For its 2010 Global Fraud Survey, Kroll talked to more than 800 senior executives, and found that only 36% of companies with links in the U.S. or the U.K.--likely exposing them to regulation under the U.S. Foreign Corrupt Practices Act or the U.K. Bribery Act--believe those laws apply to them. Another 25% said they didn't think the laws applied to them at all, while 37% were not sure.

"Companies with links to either the United States or the United Kingdom need to review their legal position and controls in order not to fall afoul of more aggressive anti-corruption enforcement," the report says.

Only a third of those surveyed believe senior managers are thoroughly familiar with the legislation, though nearly half said they have adequate procedures in place to prevent bribery at all levels.

More broadly, the survey found that 88% of respondents were hit by some form of fraud in the past year, and that information theft was the most common form, surpassing physical theft for the first time. Compared to the previous year, incidents of money laundering increased to 6% of total fraud, up from 3%. Bribery declined to 10% from 12% of total incidents.