Hodge classes are motivated conjecture

Let $k$ be an algebraically closed subfield of $\mathbf C$, let $\operatorname{AM}$ be the category of André motives over $k$, let $M\in\operatorname{AM}$, and let $r(M)$ be its realization. The Mumford--Tate group $\operatorname{MT}(r(M))$ is contained in the motivic Galois group $\operatorname{G_{mot}}(M)$. Hodge classes are motivated conjecture. One has

$$\operatorname{MT}(r(M))=\operatorname{G_{mot}}(M).$$

This is equivalent to saying that the Hodge classes arising from tensor constructions on $r(M)$ are motivated. André proved the assertion for abelian varieties, but it is open in general.