Following Laumon [10], to a nonramified l-adic local system E of rank n on a curve X one associates a complex of l-adic sheaves $_n{\cal K}_E$ on the moduli stack of rank n vector bundles on X with a section, which is cuspidal and satisfies Hecke property for E. This is a geometric counterpart of the well-known construction due to Shalika [17] and Piatetski-Shapiro [16]. We express the cohomology of the tensor product $_n{\cal K}_{E_1}\otimes {_n{\cal K}_{E_2}}$ in terms of cohomology of the symmetric powers of X. This may be considered as a geometric interpretation of the local part of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program.