Maximal coactions

A coaction δ of a locally compact group G on a C*-algebra A is maximal if a certain natural map from A x _δ G x _δ G onto A⊗K(L²(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.