Minimal Length Elements in Twisted Conjugacy Classes of Finite Coxeter Groups

Let W be a finite Coxeter group and let F be an automorphism of W that leaves the set of generators of W invariant. We establish certain properties of elements of minimal length in the F-conjugacy classes of W that allow us to define character tables for the corresponding twisted Iwahori–Hecke algebras. These results are extensions of results obtained by Geck and Pfeiffer in the case where F is trivial.