Let G be a connected reductive algebraic group over an algebraically closed field k. Lusztig (1984) partitioned G into subvarieties which play a fundamental role in the study of representation theory, the Jordan classes. An analogue partition of the Lie algebra Lie(G) into subvarieties called decomposition classes dates back to Borho-Kraft (1979). When k = C the study of geometric properties (e.g., smoothness) of a point g in the closure of a Jordan class J ⊂ G can be reduced to the study of the geometry of an element x in the closure of the union of finitely many decomposition classes in Lie(M), where M ≤ G is a connected reductive subgroup depending on g. The talk aims at introducing such objects and at generalizing this reduction procedure to the case char k > 0.