On the implementability of automorphism groups

LetA be aC*-algebra andG be a locally compact group acting as strongly continuous automorphisms onA. Let be a representation ofA then we say is a covariant representation if there exists a strongly continuous unitary representation of the group acting onH which implements the automorphisms. We give necessary and sufficient conditions on a representation ofA such that a) is subrepresentation of a covariant representation and b) is subrepresentation of a covariant representation quasi-equivalent to .