Technical Report No. 2015-3 : Lifting Representations of Finite Reductive Groups : A Character Relation

Given a connected reductive group G̃ over a finite field k, and a semisimple k-automorphism ε of G̃ of finite order, let G denote the connected part of the group of ε-fixed points. Then two of the authors have previously shown that there exists a natural lifting from series of representations of G(k) to series for G̃ (k). In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.