  Grothendieck-Chow motives of quadric hypersurfaces have provided many
insights into the theory of quadratic forms. Subsequently, the landscape of
motives of more general projective homogeneous varieties has begun to emerge.
In particular, there have been many results which relate the motive of a one
homogeneous variety to motives of other simpler or smaller ones. In this paper,
we exhibit a relationship between motives of two homogeneous varieties by
producing a natural rational map between them which becomes a projective bundle
morphism after being resolved. This allows one to use formulas for projective
bundles and blowing up to relate the motives of the two varieties. We believe
that in the future this ideas could be used to discover more relationships
between other types of homogeneous varieties.

Algebraic Geometry