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Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebrainduces an automorphism of the algebra and a mapping between its highest weightmodules. For a large class of such Dynkin diagram automorphisms, we candescribe various aspects of these maps in terms of another Kac-Moody algebra,the `orbit Lie algebra'. In particular, the generating function for the traceof the map on modules, the `twining character', is equal to a character of theorbit Lie algebra. Orbit Lie algebras and twining characters constitute acrucial step towards solving the fixed point resolution problem in conformalfield theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures  Formula (6.25) corrected. While this correction might be important in  applications of our work, the results of the paper are not affected by it. In  the present submission the "extended version" is default. In this version the  corrected formula is (6.32

From Dynkin diagram symmetries to fixed point structures