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In this paper we consider various problems involving the action of areductive group $G$ on an affine variety $V$. We prove some general rationalityresults about the $G$-orbits in $V$. In addition, we extend fundamental resultsof Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of$G$ for such general $G$-actions.  We apply our general rationality results to answer a question of Serreconcerning the behaviour of his notion of $G$-complete reducibility underseparable field extensions. Applications of our new optimality results alsoinclude a construction which allows us to associate an optimal destabilizingparabolic subgroup of $G$ to any subgroup of $G$. Finally, we use these newoptimality techniques to provide an answer to Tits' Centre Conjecture in aspecial case.

Closed Orbits and uniform S-instability in Geometric Invariant Theory