2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230061We show that each integral Borel cohomology class of a connected Lie group G can be represented by a Borel bounded cocycle if and only if the radical of G is linear. This leads to a generalization of Gromov's boundedness theorem on characteristic classes of flat bundles.46 pages, new version with added referencesAlgebraic TopologyGroup Theory57T10; 20F65.text