The Geometric Satake Correspondence for Ramified Groups
  We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the Rapoport-Zink-Pappas local models. 
Xinwen Zhu
math.RT math.NT