  We introduce and study a Rokhlin-type property for actions of finite groups
on (not necessarily unital) C*-algebras. We show that the corresponding crossed
product C*-algebras can be locally approximated by C*-algebras that are stably
isomorphic to closed two-sided ideals of the given algebra. We then use this
result to prove that several classes of C*-algebras are closed under crossed
products by finite group actions with this Rokhlin property.
