Looking at the future path of high-energy physics, a muon collider offers incomparable potential for discovery in the multi-TeV energy range. However, its development must address some relevant technological challenges, which arise from the short muon lifetime, 2.2 μs, and from the difficulty of producing large numbers of muons in groups with small emittance. The first one in particular leads to the production of the so-called Beam-induced Background (BIB), which affects the design of the machine and detector.The purpose of this contribution is to describe the expected performance of the muon system of a multipurpose muon collider detector designed to reconstruct the products of multi-TeV collisions with extreme accuracy.We are proposing a design of the muon system fully based on Micropattern Gaseous Detectors (MPGD), which foresees the combination of tracking layers based on Triple-GEM detectors, with a timing layer based on a new generation MPGD called Picosec. Picosec was developed in the last few years by the RD51 collaboration, with the aim of obtaining a fast timing (sub ns) MPGD.A dedicated R&D is ongoing to optimize such a technology for the application in a muon collider experiment, both from the detector and the mechanics point of views.This contribution will present the results obtained during the R&D of the Picosec technology for the muon collider both from laboratory tests and test beams performed in 2023. Special attention will be given to the performance obtained with different gas mixtures. Moreover, we will discuss the plans for the R&D dedicated to the muon collider.
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