@DominikAbsmeier ok, thanks!

@DominikAbsmeier Well, the operator algebras that Joachim uses are Clifford algebras, so his approach is essentially using Clifford modules anyway

@K.J.Moi I think there's a paper by John Klein that does something like this?

Maybe not as general as I remembered

Ah, I suppose you can view loop spaces as topological groups, so what he does includes parametrized spectra for connected spaces.

@RuneHaugseng Yes! That is the kind of stuff I was looking for. There is also a nice section about it in Nicolaus-Scholze paper. The section is called "Farrell-Tate cohomology"

thanks