  Let $p$ be an odd prime, $m\in {\mathbb N}$ and set $q=p^m$,
$G=\operatorname{PSL}_n(q)$. Let $\theta$ be a standard graph automorphism of
$G$, $d$ be a diagonal automorphism and $\operatorname{Fr}_q$ be the Frobenius
endomorphism of $\operatorname{PSL}_n(\overline{{\mathbb F}_q})$. We show that
every $(d\circ \theta)$-conjugacy class of a $(d\circ \theta,p)$-regular
element in $G$ is represented in some $\operatorname{Fr}_q$-stable maximal
torus and that most of them are of type D. We write out the possible exceptions
and show that, in particular, if $n\geq5$ is either odd or a multiple of $4$
and $q>7$, then all such classes are of type D. We develop general arguments to
deal with twisted classes in finite groups.

Quantum Algebra;Group Theory