Absolute Chow-Kuenneth decomposition for rational homogeneous bundles and for log homogeneous varieties

In this paper, we investigate Murre’s conjecture on the existence of a Chow–Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over a smooth variety, defined over complex numbers. Chow-K"unneth decomposition is exhibited for $Z$ whenever $S$ has a Chow–Kuenneth decomposition. The same conclusion holds for a class of log homogeneous varieties, studied by M. Brion.