  We prove that a number of classes of separable unital C*-algebras are closed
under crossed products by finite group actions with the Rokhlin property,
including:
  (1) AI algebras, AT algebras, and related classes characterized by direct
limit decompositions using semiprojective building blocks.
  (2) Simple unital AH algebras with slow dimension growth and real rank zero.
  (3) C*-algebras with real rank zero or stable rank one.
  (4) C*-algebras whose quotients all satisfy the Universal Coefficient
Theorem.
  Along the way, we give a systematic treatment of the derivation of direct
limit decompositions from local approximation conditions by homomorphic images
which are not necessarily injective.
