Does the IRS have jurisdiction of a U.S. Resident Alien (NOT a U.S. citizen) trading from outside the U.S. (even if the account is with a U.S. broker)???
A "U.S. Resident Alien" - by definition - is a US resident! As such, he is subject to US taxation on his world-wide income. Very easy.
If you have been granted legal residence then uncle sam owns you even if you have gone back to your country of origin.The IRS will probably require that you get something from us immigration which says that you have lost your residency.Otherwise they will continue to demand their cut.If you are paying taxes to a tax treaty country then it can be arranged that you dont pay double.
As long as you keep your "US residency" - you pay taxes in the US. By the way: why not ask the IRS? They could tell you! No need to guess around!
taxes on your US income, yes. taxes on income from outside US - as resident alien, you would truly be an idiot to declare it, regardless of what the irs says.