Nonstable K-theory for Z-stable C*-algebras

Abstract

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, π_i(U(A)) = K_{i-1}(A) for all integers i >= 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C^*-algebras.