  We associate to outer automorphisms of generalized Kac-Moody algebras
generalized character-valued indices, the twining characters. A character
formula for twining characters is derived which shows that they coincide with
the ordinary characters of some other generalized Kac-Moody algebra, the
so-called orbit Lie algebra. Some applications to problems in conformal field
theory, algebraic geometry and the theory of sporadic simple groups are
sketched.
