  Steinberg's tensor product theorem shows that for semisimple algebraic groups
the study of irreducible representations of higher Frobenius kernels reduces to
the study of irreducible representations of the first Frobenius kernel. In the
preceding paper in this series, deforming the distribution algebra of a higher
Frobenius kernel yielded a family of deformations called higher reduced
enveloping algebras. In this paper we prove that Steinberg decomposition can be
similarly deformed, allowing us to reduce representation theoretic questions
about these algebras to questions about reduced enveloping algebras. We use
this to derive structural results about modules over these algebras.
Separately, we also show that many of the results in the preceding paper hold
without an assumption of reductivity.
