  Let $R$ be a ring with Gwgldim$(R)<\infty$. We obtain a triangle-equivalence
$\mathrm{K}(R\text{-}\mathrm{GProj})\simeq \mathrm{K}(R\text{-}\mathrm{GInj})$
which restricts to a triangle-equivalence $\mathrm{K}(R\text{-}\mathrm{Proj})$
$\simeq \mathrm{K}(R\text{-}\mathrm{Inj})$. This class of rings includes, among
others, (left) Gorenstein rings, Ding-Chen rings and the more general
Gorenstein $n$-coherent rings ($n\in \mathbb{N}\cup \{\infty\}, n\geq 2$). As
application, we establish some triangle-equivalences of Grothendieck duality
over Ding-Chen rings and Gorenstein $n$-coherent rings.
