Are there any hurdles or pitfalls to be aware of here? I'm having trouble finding any information on this topic, but I know there are various restrictions on foreign investments.
There are (almost certainly) tax implications, seek advice come tax day. Don't just go the TurboTax route. You'll either be leaving money on the table or setting yourself up for a costly problem a few years down the road.
There are good ones available, a quick internet search will help.
As long as you report the investment in a timely manner, there are no issues. Secondly, make sure to run everything by a local lawyer/Company Secretary