On the Chow Ring of the Classifying Space of some Chevalley Groups

Let $p$ be a prime and $q$ be a power of $p$. We compute the Chow ring of the classifying space of some Chevalley groups $G(\mathbb{F}_q)$, when considered as a finite algebraic group over a field of characteristic $p$ containing $\mathbb{F}_q$. Using specialization from characteristic $0$ to characteristic $p$ we also obtain results over the complex numbers.