  The fixed point resolution problem is solved for diagonal coset theories. The
primary fields into which the fixed points are resolved are described by
submodules of the branching spaces, obtained as eigenspaces of the
automorphisms that implement field identification. To compute the characters
and the modular S-matrix we use `orbit Lie algebras' and `twining characters',
which were introduced in a previous paper (hep-th/9506135). The characters of
the primary fields are expressed in terms of branching functions of twining
characters. This allows us to express the modular S-matrix through the
S-matrices of the orbit Lie algebras associated to the identification group.
Our results can be extended to the larger class of `generalized diagonal
cosets'.
