  We consider Frobenius algebras and their bimodules in certain abelian
monoidal categories. In particular we study the Picard group of the category of
bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of
invertible bimodules. The Rosenberg-Zelinsky sequence describes a homomorphism
from the group of algebra automorphisms to the Picard group, which however is
typically not surjective. We investigate under which conditions there exists a
Morita equivalent Frobenius algebra for which the corresponding homomorphism is
surjective. One motivation for our considerations is the orbifold construction
in conformal field theory.
