  For any finite-dimensional Hopf algebra $H$ we construct a group homomorphism
$\biga(H)\to \text{BrPic}(\Rep(H))$, from the group of equivalence classes of
$H$-biGalois objects to the group of equivalence classes of invertible exact
$\Rep(H)$-bimodule categories. We discuss the injectivity of this map. We
exemplify in the case $H=T_q$ is a Taft Hopf algebra and for this we classify
all exact indecomposable $\Rep(T_q)$-bimodule categories.
