  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, \pi_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.
