G-displays of Hodge type and formal p-divisible groups

Let G be a reductive group scheme over the p-adic integers, and let $$\mu $$ minuscule cocharacter for G. In Hodge-type case, we construct functor from nilpotent $$(G,\mu )$$ -displays p-nilpotent rings R to formal p-divisible groups equipped with crystalline Tate tensors. When R/pR has p-basis étale locally, show that this defines an equivalence between two categories. The definition of relies on construction G-crystal associated any adjoint -display, which extends Dieudonné crystal Zink display. As application, obtain explicit comparison Rapoport-Zink functors Hodge type defined by Kim Bültel Pappas.