  A coaction d of a locally compact group G on a C*-algebra A is maximal if a
certain natural map from A times_d G times_{d hat} G onto A otimes K(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.
