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In this paper, we investigate Murre's conjecture on the existence of aChow--Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over asmooth variety, defined over complex numbers. Chow-K\"unneth decomposition isexhibited for $Z$ whenever $S$ has a Chow--Kuenneth decomposition. The sameconclusion holds for a class of log homogeneous varieties, studied by M. Brion.

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