Induction in stages for crossed products of C∗-algebras by maximal coactions ✩

Let δ be a maximal coaction of a locally compact group G on a C∗-algebra B, and let N and H be closed normal subgroups of G with N ⊆ H. We show that the process IndG G/H which uses Mansfield’s bimodule to induce representations of B δ G from those of B δ| (G/H) is equivalent to the two-stage induction process IndG G/N ◦IndG/N G/H . The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces. © 2007 Elsevier Inc. All rights reserved.