Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groups

Let $G$ be a compact Lie group with a maximal torus $T$. Based on a presentation of the integral cohomology ring $H^{\ast }(G\mathrm{/}T)$ of the flag manifold $G\mathrm{/}T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit and unified construction of the integral cohomology rings $H^{\ast }(G)$ for the $1$–connected Lie groups $G$. In this paper we extend this construction to all compact Lie groups.