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 the associated $C^\ast$-category
depends functorially on the group. Thus the $K$-theory spectrum of the reduced
group $C^\ast$-algebra is a functor.