Duality of restriction and induction for C*-coactions

Consider a coaction delta of a locally compact group G on a C*- algebra A, and a closed normal subgroup N of G. We prove, following results of Echterhoff for abelian G, that Mansfield's imprimitivity between A x (delta\) GIN and A x (delta) G x (<(delta)over cap>,r) N implements equivalences between Mansfield induction of representations from A x delta\ G/N to A x (delta) G and restriction of representations from A x (delta) G x (<(delta over cap>),r) N to A x delta G, and between restriction of representations from A x (delta) G to A x (delta\) G/N and Green induction of representations from A x(delta) G to A x(delta) G x(<(delta)over cap>,r) N. This allows us to deduce properties of Mansfield induction from the known theory of ordinary crossed products.