Crossed products by finite group actions with the Rokhlin property
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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.
22 pages; AMSLaTeX. Changes for version 3: One theorem (on ideals in crossed products by the Rokhlin property) removed; it will appear in a different paper. Minor improvements. Changes for version 2: Substantial expansion
22 pages; AMSLaTeX. Changes for version 3: One theorem (on ideals in crossed products by the Rokhlin property) removed; it will appear in a different paper. Minor improvements. Changes for version 2: Substantial expansion