  For a reductive group $G$ we equip the category of
$G_\mathcal{O}$-equivariant polarizable pure Hodge modules on the affine
Grassmannian $\mathrm{Gr}_G$ with a structure of neutral Tannakian category. We
show that it is equivalent to a twisted tensor product of the category of
representations of the Langlands dual group and the category of pure
polarizable Hodge structures.
