In this paper we consider the following critical nonlocal problem, where s∈(0, 1), Ω is an open bounded subset of Rn, n>2s, with continuous boundary, λ is a positive real parameter, 2*:=2n/(n-2s) is the fractional critical Sobolev exponent, while LK is the nonlocal integrodifferential operator, whose model is given by the fractional Laplacian -(-δ)s.Along the paper, we prove a multiplicity and bifurcation result for this problem, using a classical theorem in critical points theory. Precisely, we show that in a suitable left neighborhood of any eigenvalue of -LK (with Dirichlet boundary data) the number of nontrivial solutions for the problem under consideration is at least twice the multiplicity of the eigenvalue. 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