We use Green-Riefel machinary to induce representations from a closed subgroupoid crossed product to the groupoid crossed product with a lower semicontinuous bundle of C∗-algebras .

Suppose N is a closed normal subgroup of a locally compact group G. A coaction e: A —» M(A ® C*(N)) of N on a C*-algebra A can be inflated to a coaction S of G on A , and the crossed product A x¿ G is then isomorphic to the induced C*-algebra Ind^A xe N . We prove this and a natural generalization in which A xf N is replaced by a twisted crossed product A x G/N G ; in case G is abelian, we reco...

Let p be an odd prime. In this paper we study the relationship between degeneracy and decomposability in abelian crossed products. In particular we construct an indecomposable abelian crossed product division algebra of exponent p and index p. The algebra we construct is generic in the sense of [AS78] and has the property that its underlying abelian crossed product is a decomposable division al...