Motivic cohomology of the simplicial motive of a Rost variety (Q979065)

The authors compute motivic cohomology groups of the simplicial motive \(\mathcal X_{\theta}\) of a Rost variety for an \(n\)-symbol \(\theta\) in Galois cohomology of a field. As an application the authors compute the kernel and cokernel of multiplication by \(\theta\) in Galois cohomology. The authors also show that the reduced norm map on \(K_2\)-group of a division algebra of square-free degree is injective.