Lannes’s T–functor and equivariant Chow rings

For $X$ a smooth scheme acted on by linear algebraic group $G$ and $p$ prime, the equivariant Chow ring $CH^*_G(X)\otimes \mathbb{F}_p$ is an unstable algebra over Steenrod algebra. We compute Lannes's $T$-functor applied to \mathbb{F}_p$. As application, we localization of away from $n$-nilpotent modules algebra, affirming conjecture Totaro as special case. The case when point $n = 1$ generalizes recovers algebro-geometric version Quillen's stratification theorem proved Yagita Totaro.