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For any maximal coaction (A, G, delta) and any closed normal subgroup N of G,there exists an imprimitivity bimodule Y between the full crossed product A x Gx N and A x G/N, together with a compatible coaction delta_Y of G. Theassignment (A, delta) -> (Y, delta_Y) implements a natural equivalence betweenthe crossed-product functors "x G x N" and "x G/N", in the category whoseobjects are maximal coactions of G and whose morphisms are isomorphism classesof right-Hilbert bimodule coactions of G.

Mansfield’s imprimitivity theorem for full crossed products