INDUCED C-ASTERISK-ALGEBRAS AND LANDSTAD DUALITY FOR TWISTED COACTIONS

Suppose N is a closed normal subgroup of a locally compact group G. A coaction epsilon: A --> M(A X C(N)) of N on a C*-algebra A can be inf lated to a coaction delta of G on A, and the crossed product A x delta G is then isomorphic to the induced C-algebra Ind(N)(G)A x(epsilon) N. We prove this and a natural generalization in which A x, N is repla ced by a twisted crossed product A x (G/N) G; in case G is abelian, we recover a theorem of Olesen and Pedersen. We then use this to extend the Landstad duality of the first author to twisted crossed products, and give several applications. In particular, we prove that if 1 --> N --> G --> G/N --> 1 is topologically trivial, but not necessarily spl it as a group extension, then every twisted crossed product A x(G/N) G is isomorphic to a crossed product of the form A x N.