AF embeddability of crossed products of AF algebras by the integers

If A is an AF algebra and alpha is an element of Aut(A), it is shown that AF embeddability of the crossed product, A x(alpha) Z, is equivalent to A x(alpha) Z being stably finite. This equivalence follows from a simple K-theoretic characterization of AF embeddability. it is then shown that if A x(alpha) Z is AF embeddable, then the AF embedding can be chosen in such a way as to induce a rationally injective map on K-0(A x(alpha) Z). (C) 1998 Academic Press.