  In this paper we define the triangulated category of motives over a
simplicial scheme. The morphisms between the Tate objects in this category
compute the motivic cohomology of the underlying scheme. In the last section we
consider the special case of "embedded" simplicial schemes, which correspond to
the subsheaves of the constant sheaf and naturally appear in the descent
problems for motivic cohomology such as the Bloch-Kato conjecture.
