An example of the derived geometrical Satake correspondence over integers

Let G^v be a complex simple algebraic group. We describe certain morphisms of G^v (O)-equivariant complexes of sheaves on the affine Grassmannian Gr of G^v in terms of certain morphisms of G-equivariant coherent sheaves on g, where G is the Langlands dual group of G^v and g is its Lie algebra. This can be regarded as an example of the derived Satake correspondence.