  Let $G$ be a semisimple algebraic group over an algebraically closed field
$k$ of positive characteristic $p$. Under some restrictions on the size of $p$,
the present paper establishes new results on the $G$-module structure of
$\Ext^\bullet_{G_1}(V,W)$ when $V,W$ belong to several important classes of
rational $G$-modules, and $G_1$ denotes the first Frobenius kernel of $G$. For
example, it is proved that, if $L,L'$ are ($p$-regular) irreducible
$G_1$-modules, then $\Ext^n_{G_1}(L,L')^{[-1]}$ has a good filtration with
computable multiplicities. This and many other results depend on the entirely
new technique of using methods of what we call forced gradings in the
representation theory of $G$, as developed by the authors in recent papers, and
extended here.
  In addition to providing proofs, these methods lead effectively to a new
conceptual framework for the study of rational $G$-modules, and, in this
context, to the introduction of a new class of graded finite dimensional
algebras, which we call Q-Koszul algebras. These algebras are similar to Koszul
algebras, but are quasi-hereditary, rather than semisimple, in grade 0.
