A technique for computing oriented cohomology rings of semisimple algebraic groups

We present a technique for computing a finite set of generators and relations for the ring $\mathrm{h}^*(G)$ in terms of formal Demazure operators, where $\mathrm{h}^*$ is an oriented cohomology theory satisfying the localization axiom and $G$ is a semisimple algebraic group.

Using this technique, we give minimal presentations for the oriented cohomology rings of the adjoint and simply-connected groups of types $A_1$, $A_2$, and $B_2$.