Just want to share my experience. I am belorussian nationality (Belarus is COP) traveled to Ukraine. The passport control in Kiev took just a few minutes. I haven't event showed my Green Card. On the way back I showed my Byelorussian passport and my GC. The officer was a young female, probably unexperienced, ask her supervisor if I was OK to go and he just said " Does he have a Green Card". She said yes and he said: " Than he is absolutely OK to go". For those young males under 27 who are came from other countries of post Soviet Union and are consirned about army, they pretty much don't give a shit.