AF Embeddability of Crossed Products of AF Algebras by the Integers

IfAis an AF algebra andα∈Aut(A), it is shown that AF embeddability of the crossed product,A×αZ, is equivalent toA×αZ being stably finite. This equivalence follows from a simple K-theoretic characterization of AF embeddability. It is then shown that ifA×αZ is AF embeddable, then the AF embedding can be chosen in such a way as to induce a rationally injective map onK0(A×αZ).