For any Bott-Samelson resolution $q_{ I}:\hat{ X_{ I}}\rightarrow G/B$ of the flag variety $G/B$, and any torus equivariant oriented cohomology $h_T$, we compute the restriction formula of certain basis $\eta_L$ of $h_T(\hat{ X_{ I}})$ determined by the projective bundle formula. As an application, we show that $h_T(\hat{ X_{ I}})$ embeds into the equivariant oriented cohomology of $T$-fixed points, and the image can be characterized by using the Goresky-Kottwitz-MacPherson (GKM) description. Furthermore, we compute the push-forward of the basis $\eta_L$ onto $h_T(G/B)$, and their restriction formula.
Categories: math.AG math.RA