  An important breakthrough in understanding the geometry of Schubert varieties
was the introduction of the notion of Frobenius split varieties and the result
that the flag varieties G/P are Frobenius split. The aim of this article is to
give in this case a complete and self contained representation theoretic
approach to this method. The geometric Frobenius method in (char k=p>0) will
here be replaced by Lusztig's Frobenius maps for quantum groups at roots of
unity (which exist not only for primes but any odd integer \ell >1).
