Chow rings of nonabelian p-groups of order p³

Abstract

Let G be a nonabelian p group of order p³ (i.e., extraspecial p-group), and BG its classifying space. Then CH^*(BG) ≅ H^2*(BG) where CH^*(–) is the Chow ring over the field k = C. We also compute mod(2) motivic cohomology and motivic cobordism of BQ₈ and BD₈.