Cell decomposition of some unitary group Rapoport-Zink spaces

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In this paper we study the p-adic analytic geometry of the basic unitary group Rapoport-Zink spaces ₖ with signature (1,n-1). Using the theory of Harder-Narasimhan filtration of finite flat groups developed by Fargues in F2,F3, and the Bruhat-Tits stratification of the reduced special fiber defined by Vollaard-Wedhorn in VW, we find some relatively compact fundamental domain ₖ in ₖ for the action of G(ₚ)× Jb(ₚ), the product of the associated p-adic reductive groups, and prove that ₖ admits a locally finite cell decomposition. By considering the action of regular elliptic elements on these cells, we establish a Lefschetz trace formula for these spaces by applying Mieda's main theorem in Mi2.