ABB is cooperating with the U.S. Justice Department regarding suspect payments that it made in at least one middle eastern country. The question that may come to mind is why the U.S. Foreign Corrupt Practices Act would seem to apply to actions by a Swedish/Swiss corporation in the middle east. The answer is that, by registering under the Securities Exchange Act of 1934 in order to list on the New York Stock Exchange, ABB subjected itself to the FCPA. There is still an interesting question, which no doubt ABB lawyers are considering, whether non-U.S. ABB subsidiaries are subject to the FCPA.
The application of the FCPA to companies that list on a U.S. exchange has not been the subject (as far as I have heard) of substantial criticism as "extraterritorial." And, of course, with the recent advent of the OECD convention on bribery, other wealthy states are to have similar rules.