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 ${\mathrm{h}}^{\ast }(G)$ in terms of formal Demazure operators, where ${\mathrm{h}}^{\ast }$ 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 $B_2$.