  In this paper we study the simplicial complex induced by the poset of Brauer
pairs ordered by inclusion for the family of finite reductive groups. In the
defining characteristic case, the homotopy type of this simplicial complex
coincides with that of the Tits building thanks to a well-known result of
Quillen. On the other hand, in the non-defining characteristic case, we show
that the simplicial complex of Brauer pairs is homotopy equivalent to a
simplicial complex determined by generalised Harish-Chandra theory. This
extends earlier results of the author on the Brown complex and makes use of the
theory of connected subpairs and twisted block induction developed by Cabanes
and Enguehard.

Representation Theory;Algebraic Topology;Group Theory