  We prove that the symmetric monoidal category of mixed motives generated by
an abelian variety (more generally, an abelian scheme) can be described as a
certain module category. More precisely, we describe it as the category of
quasi-coherent complexes over a derived quotient stack constructed from a
motivic algebra of the abelian variety. We then study the structure of the
motivic Galois groups of their mixed motives. We prove that the motivic Galois
group is decomposed into a unipotent part constructed from the motivic algebra,
and the reductive quotient which is the Tannaka dual of Grothendieck numerical
motives.
