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Let Γ be a finite group acting linearly on a vector space V . We compute the Lie algebra cohomology of the Lie algebra of Γ-invariant formal vector fields on V . We use this computation to define characteristic classes for foliations on orbifolds. 2.1. Eigenvalues of the Euler field. We point out that the Γ action on V can be made unitary 3 . Accordingly, as unitary representations of Γ are completely reducible, 1 This notation is a possible source of confusion as it is also used to denote thedoi:10.4310/mrl.2008.v15.n1.a12 fatcat:y6ihspb6rzd2vdjexar4x3o24a