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).