Induced coactions of discrete groups on C*-algebras

Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C* -coaction delta: D --> D x C*(G/N) of a quotient group G/N of a discrete group G to a C* -coaction Ind delta: Ind D --> Ind D x C*(G) of G. We show that induced coactions be have in many respects similarly to induced actions. In particular, as an an alogue of the well known imprimitivity theorem for induced actions we prove that the crossed products Ind D x(lnd delta) G and D x(delta) G/N are alwa ys Morita equivalent. We also obtain nonabelian analogues of a theorem of O lesen and Pedersen which show that there is a duality between induced coact ions and twisted actions in the sense of Green. We further investigate amen ability of Fell bundles corresponding to induced coactions.