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Let R be a discrete valuation ring with fraction field K and X a flat R-scheme. Given a faithful action of a K-group scheme G K over the generic fibre X K , we study models G of G K acting on X. In various situations, we prove that if such a model G exists, then there exists another model G ′ that acts faithfully on X. This model is the schematic closure of G inside the fppf sheaf Aut R (X) ; the major difficulty is to prove that it is representable by a scheme. For example, this holds if X isdoi:10.1090/s1056-3911-2011-00561-4 fatcat:faoe7vnph5aedn7lmewmqqsire