S. Kaliszewski et al., DUALITY OF RESTRICTION AND INDUCTION FOR C-ASTERISK-COACTIONS, Transactions of the American Mathematical Society, 349(5), 1997, pp. 2085-2113
Consider a coaction delta of a locally compact group G on a C- algebr
a 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 d
elta\ 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 rest
riction 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 Mansfi
eld induction from the known theory of ordinary crossed products.