The general theme of this talk is understanding the possible actions of a group on closed manifolds. When the group is a lattice in a higher-rank semisimple Lie group, it is expected that all possible actions are combinations of those inherited from the Lie group itself. While this has been proved in a few cases, it remains largely open in general. We will examine a specific situation where the manifolds carry a flag structure and the actions preserve that structure, leading to a classification of such actions. This talk is based on joint work with Vincent Pecastaing.