Topological methods for<i>C</i>^∗-algebras. IV. mod<i>p</i>homology

Abstract

Let h^ be a homology theory on an admissible category of C*-algebras. We define a homology theory h^-Z/n) which fits into a Bockstein exact sequence h/Z/) A Let p be a prime. If p is odd or if h^ is "good" then h^(A\ Z/p) is a Z/p-moxAe and (with finiteness assumptions on the torsion of h^(A)) there is a Bockstein spectral sequence with E\ -h^(A;Z/p) which converges to (h^(A)/(torsion)) Z/p. In the special case of A-theory, we show that K^(A <S> N) = K^(A; Z/n), provided that K 0 (N) = Z/n, K X (N) -0, and iV is in a certain (large) category ft of separable nuclear C*-algebras.