  A Morita class of symmetric special Frobenius algebras A in the modular
tensor category of a chiral CFT determines a full CFT on oriented world sheets.
For unoriented world sheets, A must in addition possess a reversion, i.e. an
isomorphism from A^opp to A squaring to the twist. Any two reversions of an
algebra A differ by an element of the group Aut(A) of algebra automorphisms of
A. We establish a group homomorphism from Aut(A) to the Picard group of the
bimodule category C_AA, with kernel consisting of the inner automorphisms, and
we refine Morita equivalence to an equivalence relation between algebras with
reversion.
