Schubert calculus in Lie groups

Let $G$ be a Lie group with a maximal torus $T$. Combining Schubert calculus in the flag manifold $G\mathrm{/}T$ with the Serre spectral sequence of the fibration $G\to G\mathrm{/}T$, we construct the integral cohomology ring $H^{\ast }(G)$ uniformly for all compact and simply connected Lie groups $G$.