  We show that the Grothendieck-Chow motive of a smooth hyperplane section $Y$
of an inner twisted form $X$ of a Milnor hypersurface splits as a direct sum of
shifted copies of the motive of the Severi-Brauer variety of the associated
cyclic algebra $A$ and the motive of its maximal commutative subfield $L\subset
A$. The proof is based on the non-triviality of the (monodromy) Galois action
on the equivariant Chow group of $Y_L$.
