A generalization of Wilkerson’s mod $p$ decompositions of compact, connected, semi-simple Lie groups  to the non-simply connected case is given. As an application, H-spaces with interesting fundamental groups are constructed.
"Mod $p$ decompositions of non-simply connected Lie groups." J. Math. Kyoto Univ. 48 (1) 1 - 5, 2008. https://doi.org/10.1215/kjm/1250280972