I want to ask whether a country can try a citizen (or a PR) for a crime not committed under their jurisdiction, provided that such country has no extraterritorial jurisdiction over its own citizens or PRs and in the case whether the act is a crime either in the citizen's country, country it's been committed in or both. I'm assuming that the country's citizen has no explicit law on extraterritorial jurisdiction, otherwise all the premise of this question would just crumble.
I'm not talking about extradition, since I'm not mentioning it and since I'm assuming not occurring in that case, but rather I'm assuming if the citizen's country knows that such person committed a crime elsewhere and extradition doesn't occur, and provided also the condition above (no extraterritorial jurisdiction), is the country allowed to try such a person theoretically? (I know that the practice is very different, maybe international laws would be ignored an bypassed by the principle of sovereignity and internal affairs when it comes to a citizen and blah blah)
I'm asking under general principles of international law, and moreover I'm asking under circumstances that erase completely the mileage of cases that may result for every different couple of countries (so " it depends on the countries involved" is not an answer) AND the theoretical chance of getting condemned in the other country, which are no extraterritorial jurisdiction and no extradition occurring, but just reporting signalation and nothing more, not even the requesting country asking for a trial to the host country against the perpetrator.