Maximal coactions

A coaction delta of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x (delta)G x ((delta) over cap)G onto Acircle timesK(L-2(G)) is an isomorphism. All dual coactions on full crossed products by group actions are maximal; a discrete coaction is maximal if and only if A is the full cross-sectional algebra of the corresponding Fell bundle. For every nondegenerate coaction of G on A, there is a maximal coaction of G on an extension of A such that the quotient map induces an isomorphism of the crossed products.