We give a complete classification up to conjugacy of the actions of a finite group G on the hyperfinite II₁ factor R in terms of three invariants : a normal subgroup N of G ; an element of the relative cohomology group H²(G/N, G, R/Z) and an element of the quotient of a finite dimensional simplex by a simplicial action of H¹(N, R / Z)^G coming from permutations of the vertices. All values of the invariants are realized by actions of G on R.