We develop a Tannakian framework for group-theoretic analogs of displays,

originally introduced by Bültel and Pappas, and further studied by Lau. We use

this framework to define Rapoport-Zink functors associated to triples (G, {μ}, [b]),

where G is a flat affine group scheme over Zp and μ is a cocharacter of G defined over

a finite unramified extension of Zp. We prove these functors give a quotient stack

presented by Witt vector loop groups, thereby showing our definition generalizes

the group-theoretic definition of Rapoport-Zink spaces given by Bültel and Pappas.

As an application, we prove a special case of a conjecture of Bültel and Pappas by

showing their definition coincides with that of Rapoport and Zink in the case of

unramified EL-type local Shimura data.