  The notion of H-covariant strong Morita equivalence is introduced for
*-algebras over C = R(i) with an ordered ring R which are equipped with a
*-action of a Hopf *-algebra H. This defines a corresponding H-covariant strong
Picard groupoid which encodes the entire Morita theory. Dropping the positivity
conditions one obtains H-covariant *-Morita equivalence with its H-covariant
*-Picard groupoid. We discuss various groupoid morphisms between the
corresponding notions of the Picard groupoids. Moreover, we realize several
Morita invariants in this context as arising from actions of the H-covariant
strong Picard groupoid. Crossed products and their Morita theory are
investigated using a groupoid morphism from the H-covariant strong Picard
groupoid into the strong Picard groupoid of the crossed products.
