We have previously shown that, when a finite group G acts on a polynomial ring S over a finite field k, only a finite number of isomorphism classes of indecomposable kG-modules occur as summands of S. We have also shown that the regularity of the invariant subring S^G is at most 0, which has various consequences. For example, that S^G is generated in degrees at most n(|G|-1), provided n, |G| >= 2. Both of these results depend on the Structure Theorem of Karaguenzian and myself, which is proved by means of a long and complicated calculation. The aim of this talk is to sketch a proof that uses a more conceptual method.