The integral geometric Satake equivalence in mixed characteristic

Let k be an algebraically closed field of characteristic p. Denote by W(k) the ring of Witt vectors of k. Let F denote a totally ramified finite extension of W(k)[1/p] and O its ring of integers. For a connected reductive group scheme G over O, we study the category P_(L+G)(Gr_G,Λ) of L+G-equivariant perverse sheaves in Λ-coefficient on the Witt vector affine Grassmannian Gr_G where Λ=Z_l and F_l(l≠p), and prove that it is equivalent as a tensor category to the category of finitely generated Λ-representations of the Langlands dual group of G.