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Mansfield’s imprimitivity theorem for full crossed products

For any maximal coaction (A, G, S) and any closed normal subgroup N of G, there exists an imprimitivity bimodule Y G G/N (A) between the full crossed product A × δ G × δ| N and A × δ| G/N, together with Inf δ| - δ dec compatible coaction Sy of G. The assignment (A,δ) → (Y G G/N (A), δ Y ) implements a natural equivalence between the crossed-product functors x G x N and x G/N, in the category whose objects are maximal coactions of G and whose morphisms are isomorphism classes of right-Hilbert bimodule coactions of G.