  Let $R$ be a two-sided noetherian ring and $M$ be a nilpotent $R$-bimodule,
which is finitely generated on both sides. We study Gorenstein homological
properties of the tensor ring $T_R(M)$. Under certain conditions, the ring $R$
is Gorenstein if and only if so is $T_R(M)$. We characterize Gorenstein
projective $T_R(M)$-modules in terms of $R$-modules.
