F-conjugacy invariance of Deligne–Lusztig cohomology

Let ${\bf t}\in B^+$, and let $F$ act on $B^+$ as in the definition of $F$-conjugacy. Two elements are $F$-conjugate if ${\bf t}'={\bf w}^{-1}{\bf t}F({\bf w})$ for some ${\bf w}\in B$. The graded $({\bf G}^F\times\langle F^\delta\rangle)$-module $H_c^*({\bf X}({\bf t}))$ is considered up to isomorphism. F-conjugacy invariance conjecture. The isomorphism class of $H_c^*({\bf X}({\bf t}))$ depends only on the $F$-conjugacy class of ${\bf t}\in B^+$.