Note on restriction maps of Chow rings to Weyl group invariants

Abstract

Let G be an algebraic group over C corresponding a compact simply connected Lie group. When H*(G) has p-torsion, we see ρ*_CH: CH*(BG) → CH*(BT)^W_G(T) is always not surjective. We also study the algebraic cobordism version ρ*_Ω. In particular when G = Spin(7) and p = 2, we see each Griffiths element in CH*(BG) is detected by an element in Ω*(BT).