  We consider quotients of the unit cube semigroup algebra by particular
$\mathbb{Z}_r\wr S_n$-invariant ideals. Using Gr\"obner basis methods, we show
that the resulting graded quotient algebra has a basis where each element is
indexed by colored permutations $(\pi,\epsilon)\in\mathbb{Z}_r\wr S_n$ and each
element encodes the negative descent and negative major index statistics on
$(\pi,\epsilon)$. This gives an algebraic interpretation of these statistics
which was previously unknown. This basis of the $\mathbb{Z}_r\wr S_n$-quotients
allows us to recover certain combinatorial identities involving Euler-Mahonian
distributions of statistics.
