  To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra
we associate a family of automorphisms of the algebra which act in a natural
way on the modules of the GKM algebra. We introduce the twining character of a
module which is obtained by inserting the action of such an automorphism into
the trace that appears in the ordinary character. Twining characters of
integrable highest weight modules and Verma modules satisfy a character formula
which involves a certain subgroup of the Weyl group. This subgroup is shown to
be the Weyl group of another GKM algebra, called the orbit Lie algebra, and
hence the twining characters coincide with ordinary characters of the orbit Lie
algebra.
