| We consider algebraic groups GL1(A), SL1(A), where A is a division algebra of prime degree over a field F, and associated motives in the category of motivic complexes DM( F). Following an idea of Suslin, we relate motives of GL 1(A) to the motive of Voevodsky's simplicial scheme X, associated to the Severi-Brauer variety of A, and compute the second differential in the resulting spectral sequence. We also give partial results on motive of SL 1(A) where A is of degree 3. |
