The $K$-theory spectrum of the reduced group $C^{\ast }$-algebra is a functor

Abstract

We construct $C^{\ast }$-categories that are anologues of the categories used in controlled algebraic $K$-theory. We then show that the reduced $C^{\ast }$-algebra of a finitely presented group and an associated controlled $C^{\ast }$-category have equivalent $K$-theory spectra, and that, at least in certain special cases, the associated $C^{\ast }$-category depends functorially on the group. Thus in these cases the $K$-theory spectrum of the reduced group $C^{\ast }$-algebra is a functor.

The paper has been withdrawn due to a crucial error