Classification of a class of crossed product C⁎-algebras associated with residually finite groups

A residually finite group acts on a profinite completion by left translation. We consider the corresponding crossed product C⁎-algebra for discrete countable groups that are central extensions of finitely generated abelian groups by finitely generated abelian groups (these are automatically residually finite). We prove that all such crossed products are classifiable by K-theoretic invariants using techniques from the classification theory for nuclear C⁎-algebras.