  The setting is the representation theory of a simply connected, semisimple
algebraic group over a field of positive characteristic. There is a natural
transformation from the wall-crossing functor to the identity functor. The
kernel of this transformation is a left exact functor. This functor and its
first derived functor are evaluated on the global sections of a line bundle on
the flag variety. It is conjectured that the derived functors of order greater
than one annihilate the global sections. Also, the principal indecomposable
modules for the Frobenius subgroups are shown to be acyclic.
