The etale cohomology of the general linear group over a finite field and   the Deligne and Lusztig variety
  Let $p\not =\ell$ be primes. We study the etale cohomology $H^{*}_{et}(BGL_n(\bF_{p^s});\bZ/{\ell})$ over the algebraically closed field $\bar \bF_p$ by using the stratification methods from Molina-Vistoli. To compute this cohomology, we use the Delinge-Lusztig variety. 
Michishige Tezuka and Nobuaki Yagita
math.AT