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