A Universal Multi-coefficient Theorem for the Kasparov Groups

that holds in the same generality as the universal coefficient theorem of Rosenberg and Schochet. There are advantages, in some circumstances, to using HomΛ(K(A),K(B)) in place of KK(A,B). These advantages derive from the fact that K(A) can be equipped with order and scale structures similar to those on K0(A). With this additional structure, the “Λ−module” K(A) becomes a powerful invariant of C*algebras. We show that it is a complete invariant for the class of real-rank-zero AD algebras. The AD algebras are a certain kind of approximately subhomogeneous C∗-algebras which may have torsion in K1 [Ell]. In addition to classifying these algebras, we calculate their automorphism groups up to approximately innerautomorphisms.