Resumen en español

Through a geometric approach, we explain the origin of the crepant resolution conjecture of Y. Ruan. More precisely, we calculate the Chen-Ruan cohomology and the quantum corrections of Ruan for the cohomology of Hilbert schemes in the particular case of the two-fold symmetric product of CP2, which corresponds to the invariant part by the action of the symmetric group S2 on the blow-up of CP2 × CP2 along the diagonal.