Hopf-Galois extensions and an exact sequence for $H$-Picard groups
  Let $H$ be a Hopf algebra, and $A$ an $H$-Galois extension. We investigate $H$-Morita autoequivalences of $A$, introduce the concept of $H$-Picard group, and we establish an exact sequence linking the $H$-Picard group of $A$ and the Picard group of $A^{{\rm co}H}$. 
S. Caenepeel and A. Marcus