  We propose an $r$-variable version of Kostka-Shoji polynomials
$K^-_{\lambda\mu}$ for $r$-multipartitions $\lambda,\mu$. Our version has
positive integral coefficients and encodes the graded multiplicities in the
space of global sections of a line bundle over Lusztig's iterated convolution
diagram for the cyclic quiver $\tilde{A}_{r-1}$.
