  Following Laumon [10], to a nonramified $\ell$-adic local system $E$ of rank
$n$ on a curve $X$ one associates a complex of $\ell$-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.
