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 which uses Mansfield's bimodule to induce representations of B⋊δG from those of B⋊δ|(G/H) is equivalent to the two-stage induction process . The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces.