  We generalize the basic results of Vinberg's \theta-groups, or periodically
graded reductive Lie algebras, to fields of good positive characteristic. To
this end we clarify the relationship between the little Weyl group and the
(standard) Weyl group. We deduce that the ring of invariants associated to the
grading is a polynomial ring. This approach allows us to prove the existence of
a KW-section for a classical graded Lie algebra (in zero or good
characteristic), confirming a conjecture of Popov in this case.
