I’m not sure I follow - The items were taken from somewhere at some point in time and now there is a country on that territory.

Take an extreme hypothetical. Suppose in the 1500s the government of Spain had taken some artifacts relating to the indigenous peoples of New Mexico. Would the government of the United States really be the rightful owner of these artifacts?

For other countries it's not quite as extreme, but in general the link between ancient culture in place X and modern country in place X is less strong than people try to make out.

I don’t see the controversy of your example because since there was no UNESCO and other global agreements in the 1500s, the indigenous people of this area are still around and so it would be the local Native American tribes that can have a legitimate claim on their heritage.

Lots of native american tribes committed genocide and destroyed other tribes. If Tribe A made some artifacts, and then was genocided out of existence by Tribe B, which was then conquered by the Tribe C (USA). Would you want Tribe B to have ownership of the artifacts of tribe B?

Including your 'tribe C' (the USA) with two indigenous tribes (A & B) in your example is highly disingenuous. And self-serving to your contrived hypothetical.

It is an interesting theory, if I understand it. Is the Idea that controlling a geographic region makes one the rightful heir to any artifacts created by people and cultures previously in the region?

Does the USA have a claim to all indigenous Artifacts created in the US? It doesn't seem that different than Egypt laying claim to Egyptian artifacts.

I think it’s clear the spirit of my comment was to mean that the descendants of the original owners would be one of the parties with a claim to have their artefacts repatriated. It’s clearly not a strictly geographical problem.

Are we talking genetic ancestry? What if the genetic ancestors have little in common with the current geographic population What if the genetic ancestors themselves were brutal slavers and overlords who extracted the riches by force?

This is a very good point, which I brought up in another comment. Arguing on the basis of broad genetic ancestry to establish ownership of ancient artifacts can quickly get murky and nonsensical, when considering nations that exist today with similar genetic ancestry, and also those former nations which may have been antagonistic, yet have similar genetics.

The idea of a nation-state is surprisingly recent and not completely universal, right? Historically people might be organized along kinship, tribal, ethnic, religious, or some other lines. Then an empire could pop up and control various groups of those, often against their wills, sometimes via intermediaries (which might not even map well to the underlying peoples).

I do think the best thing to do is to return artifacts to their rightful owners, but figuring out who the rightful owners is, can be quite difficult.

I mean, if they stole some artifacts from a tribe, which was subsequently wiped out by a tribe of bitter rivals, do they give their artifacts back to the rival tribe that later went on to form a government? (Just as a hypothetical, hopefully this is general enough that it is clear that I’m not trying to describe any particular real situation).

Interesting thought. Perhaps the Egyptian relics should be repatriated to modern day practitioners of Egyptian polytheism. I believe the Kemetic Orthodoxy is currently headquartered in Illinois, USA.

https://en.wikipedia.org/wiki/Kemetic_Orthodoxy#Worship

Hah. I’m going to intentionally pass on that one, my main point was that it is hard to make these decisions. The existence of surprising edge cases like yours just goes to show that it is a hard problem.

Egypt abandoned monotheism for Christianity before surrendering to Muslims.