  On the bundles of WZW chiral blocks over the moduli space of a punctured
rational curve we construct isomorphisms that implement the action of outer
automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms
respect the Knizhnik-Zamolodchikov connection and have finite order. When all
primary fields are fixed points, the isomorphisms are endomorphisms; in this
case, the bundle of chiral blocks is typically a reducible vector bundle. A
conjecture for the trace of such endomorphisms is presented; the proposed
relation generalizes the Verlinde formula. Our results have applications to
conformal field theories based on non-simply connected groups and to the
classification of boundary conditions in such theories.
