I am a citizen of the United States of America. As such, it is illegal for me to--to take an extreme example--murder. However, say I am going on vacation to a little nation where it is not illegal to murder--if you decapitate someone for stealing your oranges, the only thing that you'll have to worry about is the cleanliness of your machete.
So I am in this country when another adult cuts me in line for the roller coaster. Naturally taking this personally and as an insult, I take out my machete and swing at my adversary; after realizing that I missed the cutter altogether, I pull out my revolver and shoot my opponent, and he dies.
I have just murdered a man; however, because murder is not illegal in this country, I have done nothing (from the law's perspective) wrong.
Upon returning to the US, of which I am a citizen, can I be tried for murder even though I did not do it in the US's jurisdiction?
Does this apply to all actions that are unlawful in one jurisdiction but not another?
Thanks a lot in advance for any responses. All are greatly appreciated!