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Moduli spaces of bounded local $G$-shtukas are a group-theoreticgeneralization of the function field analog of Rapoport and Zink's modulispaces of $p$-divisible groups. In this article we generalize some veryprominent concepts in the theory of Rapoport-Zink spaces to our setting. Moreprecisely, we define period spaces, as well as the period map from a modulispace of bounded local $G$-shtukas to the corresponding period space, and wedetermine the image of the period map. Furthermore, we define a tower ofcoverings of the generic fiber of the moduli space which is equipped with aHecke action and an action of a suitable automorphism group. Finally weconsider the $\ell$-adic cohomology of these towers.

The generic fiber of moduli spaces of bounded local $G$-shtukas