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-Künneth 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.

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