Please don't go to New Haven. It's not sanitary.
From reading the article, I get the idea that:
a) Peru claims ownership of these artifacts
b) Yale refuses to acknowledge Peru's ownership, but also does not explicitly claim ownership themselves, and it attempting to negotiate favorable terms for partial repatriation of the artifacts
It's hard to escape the conclusion that Yale knows it doesn't own the artifacts, knows that Peru does, and just doesn't want to admit it because then Peru would have the right to have all the artifacts returned immediately, and Yale would lose its bargaining position.
Yale was lent the artifacts and now is trying to leverage its current possession into part ownership.