  Let G be a connected reductive group over an algebraically closed field. We
define a decomposition of G into finitely many strata such that each stratum is
a union of conjugacy classes of fixed dimension; the strata are indexed by a
set defined in terms of the Weyl group which is independent of the
characteristic. In the case where $G$ is replaced by the corresponding loop
group we define an analogous decomposition of the set of regular semisimple
compact elements into countably many strata.
