In this paper we study the p-adic analytic geometry of the basic unitary
group Rapoport–Zink spaces MK with signature (1, n − 1). Using the theory of
Harder–Narasimhan filtration of finite flat groups developed in Fargues (Journal für die
reine und angewandteMathematik 645:1–39, 2010), Fargues (Théorie de la réduction
pour les groupes p-divisibles, prépublications. http://www.math.jussieu.fr/~fargues/
Prepublications.html, 2010), and the Bruhat–Tits stratification of the reduced special
fiber Mred defined in Vollaard and Wedhorn (Invent. Math. 184:591–627, 2011),
we find some relatively compact fundamental domain DK in MK for the action of
G(Qp)×Jb(Qp), the product of the associated p-adic reductive groups, and prove that
MK 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 Mieda (Lefschetz trace formula for open adic
spaces (Preprint). arXiv:1011.1720, 2013).