The SEC has regulatory authority over any securities related activities conducted both in the United States and with US citizens. They can take a wide range of actions against violators, and have, through the years, taken action against numerous Canadian companies whose shares are not registered or traded in the US. Do anything securities related in the US or contact (either directly or indirectly) a US citizen and you fall under the SEC's jurisdiction regardless of your location. Sometimes they simply provide evidence or investigatory information to the regulators in the violator's home jurisdiction, and sometimes the SEC takes direct action on their own.
That includes individuals illegally pumping stocks, BTW.