I have a small amount of knowledge about this.
My grandmother was very good friends with an ancestor of Cher through the mother’s side but I believe this person married into the family. I can’t remember. Something like married her grandmother’s sibling or something like that.
She said there was Indian blood in the family. Now, this could have been just one of those handed down stories from generations but Cher did have reason to believe she had Indian Heritage from an anecdotal basis.
I think she later disavowed Indian Heritage.
It’s just that “cherokee” was cooler than “armenian” at the time.