The generalized Picard groups for finite dimensional C*-Hopf algebra coactions on unital C*-algebras

We shall generalize the notion of the strong Morita equivalence for coactions of a finite dimensional C*-Hopf algebra on a unital C*-algebra and define the Picard groups with respect to the generalized strong Morita equivalence. We call them the generalized Picard groups for coactions of a finite dimensional C*-Hopf algebra on a unital C*-algebra. We shall investigate basic properties of the generalized Picard groups and clarify the relation between the generalized Picard groups and the Picard groups for unital inclusions of unital C*-algebras.