Tannakian properties of unit Frobenius-modules

We show that unit OF,XΛ-modules of Emerton and Kisin provide an analogue of locally constant sheaves in the context of Böckle-Pink Λ-crystals. For example they form a tannakian category if the coefficient algebra Λ is a field. Our results hold for a big class of coefficient algebras which includes Drinfeld rings, and for arbitrary locally noetherian base schemes.