Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein
cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R-
modules, which is a “Gorenstein analogue” of weak tilting modules. It is proven that a left R-
module W is Gorenstein weak n-tilting if and only if its character module W+ is Gorenstein n-
cotilting if and only if its Gorenstein flat dimension is at most n and its left Gorenstein Tor-
orthogonal class consists precisely of all right R-modules with a G-exact right Prod (W+) …