  We compute the cohomology of modules over the algebra of twisted chiral
differential operators over the flag manifold. This is applied to (1) finding
the character of $G$-integrable irreducible highest weight modules over the
affine Lie algebra at the critical level, and (2) computing a certain elliptic
genus of the flag manifold. The main tool is a result that interprets the
Drinfeld-Sokolov reduction as a derived functor.
