Displays were introduced by Zink in the 2000s in order to generalize Dieudonné theory to arbitrary p-complete base rings. When studying Shmiura varieties and related objects one is naturally led to the task of defining group-theoretic versions of Abelian varieties and p-divisible groups. We report on results in the direction of developing a theory of (G, mu)-displays for a datum (G, mu), where G is a parahoric Zp-group scheme, extending work of Bültel-Pappas and Pappas. We furthermore give an application to the EKOR-stratification on the special fiber of a Kisin-Pappas integral Shimura variety.