Motivic decomposition conjecture for moduli spaces of vector bundles

Let $C$ be a smooth projective curve over an algebraically closed field of characteristic zero, let $L$ be a line bundle on $C$ of degree coprime to $r$, and let $M(r,L)$ be the moduli space of rank-$r$ stable vector bundles on $C$ with determinant $L$. Let $h(X)$ denote the motive of a variety $X$, and let $J(C)$ be the Jacobian of $C$. Motivic decomposition conjecture. The motive $h(M(r,L))$ can be expressed as a direct sum of motives of products of symmetric powers of $C$ and the Jacobian $J(C)$.

The conjecture proposes a motivic description of the moduli space in terms of standard varieties associated with the curve; the source does not specify a resolution status.