TY - JOUR AU - Echterhoff, Siegfried AU - Quigg, John PY - 2002/06/01 Y2 - 2024/03/28 TI - Full duality for coactions of discrete groups JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 90 IS - 2 SE - Articles DO - 10.7146/math.scand.a-14374 UR - https://www.mscand.dk/article/view/14374 SP - 267-288 AB - Using the strong relation between coactions of a discrete group $G$ on $C^*$-algebras and Fell bundles over $G$ we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of $G$ as opposed to the usual theory of [16], [11] which uses the spatially defined reduced crossed products and normal subgroups of $G$. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel [7] if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions. ER -