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is isomorphic to ℤp, there exists a continuous pp-adic character p of Γ such that, for every open subgroup U of Γ, the group of U-coinvariants M(p)U is finite; here M(p) denotes the twist of M by pp. This twisting lemma was already used to study various arithmetic properties of Selmer groups and Galois cohomologies over a cyclotomic tower by Greenberg and Perrin-Riou. We prove a noncommutative generalization of this twisting lemma, replacing torsion modules over ℤp[[Γ]] by certain torsion modules over ℤp[[G]] with more general p-adic Lie group G. 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