Images of two-dimensional motivic Galois representations

Let M be a two-dimensional motive which is pure of weight w over a number field K and let (phi(l): G(K)-->Aut(H-l(M))(l) be the system of the l-adic realizations. Choose G(K)-invariant Z(l)-lattices T-l of H-l(M) and let (phi(l): G(K)-->GL(T-l))(l) be the corresponding system of integral representations. Then either for almost all primes phi(l)(G(K)) consist of all the elements of GL(T-l) with determinant in (Z*(l))(-w) or the system (phi(l)) is associated to algebraic Hecke characters. We also can prove an adelic version of our results.