  We consider algebraic groups GL_1(A), SL_1(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
these groups to the motive of Voevodsky's simplicial scheme X, associated to
the Severi-Brauer variety of A.
