  Let $W$ be a finite Weyl group and $\sg$ be a non-trivial graph automorphism
of $W$. We show a remarkable relation between the $\sg$-twisted involution
module for $W$ and the Frobenius--Schur indicators of the unipotent characters
of a corresponding twisted finite group of Lie type. This extends earlier
results of Lusztig-Vogan for the untwisted case and then allows us to state a
general result valid for any finite group of Lie type. Inspired by recent work
of Marberg, we also formally define Frobenius--Schur indicators for "unipotent
characters" of twisted dihedral groups.
