  Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra
induces an automorphism of the algebra and a mapping between its highest weight
modules. For a large class of such Dynkin diagram automorphisms, we can
describe various aspects of these maps in terms of another Kac-Moody algebra,
the `orbit Lie algebra'. In particular, the generating function for the trace
of the map on modules, the `twining character', is equal to a character of the
orbit Lie algebra. Orbit Lie algebras and twining characters constitute a
crucial step towards solving the fixed point resolution problem in conformal
field theory.
