  We describe the cohomology of the sheaf of twisted differential operators on
the quantized flag manifold at a root of unity whose order is a prime power. It
follows from this and our previous results that for the De Concini-Kac type
quantized enveloping algebra, where the parameter $q$ is specialized to a root
of unity whose order is a prime power, the number of irreducible modules with a
certain specified central character coincides with the dimension of the total
cohomology group of the corresponding Springer fiber. This gives a weak version
of a conjecture of Lusztig concerning non-restricted representations of the
quantized enveloping algebra.
