2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155272We compute $CH^*BG_2$ and $CH^*BSpin_7$, using in particular the stratification method introduced by Vezzosi. We also give some information on the Chow rings of the finite groups $G_2(q)$. This new version includes an appendix, which will be published on its own as an addendum. It explains how one can use our results to produce a counter-example to the conjecture, due to Totaro, which predicted that the Chow ring of a finite group was generated by transfers of Chern classes.21 pagesAlgebraic GeometryAlgebraic Topologytext