  As shown by Bonnaf\'e, a step in proving a Jordan decomposition of characters
of finite special linear groups is the parametrization of unipotent characters
of centralizers of semi-simple elements in projective linear groups. We show
the same kind of result in the case of finite special unitary groups. The proof
leads to a mild adaptation of Bonnaf\'e's methods expounded in [B99]. The
outcome is a Jordan decomposition of characters compatible with Lusztig's
twisted induction.
