Can Yaylali (Darmstadt/Paris)

Abstract: A finite reductive group G^F is defined as the fixed points of a reductive group G/F_q under the q-Frobenius endomorphism. Their representations were studied by Deligne-Lusztig and Brokemper gave a description of the G^F-equivariant intersection ring of a point (the ring classifying G^F-invariant cycles). Focusing on the latter, I will give an introduction to (rational) motives with group actions and how this is related to equivariant intersection theory. I will use this formalism to relate motives with G^F-action to equivariant motives on the associated flag variety. I will also explain how this relates to Brokemper’s computations on algebraic cycles. If time permits, I will try to discuss the implications on l-adic cohomology and how this can be used in the future to study motivic representation theory of G^F following Deligne-Lusztig.