Gorenstein derived functors

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Existence of Gorenstein projective resolutions and Tate cohomology (2007, background): “Note that Ext iG (−, −) is a well defined bifunctor; see [3] or [11] for this and other properties.”
Beyond totally reflexive modules and back (2008, methodology): “The question of balancedness for relative (co)homology is treated by Enochs and Jenda [43], Holm [65], and Iacob [74].”
Gorenstein projective dimension for complexes (2004, background): “Our purpose here is to show that the result of [6] extend to the general setup of [19].”
Generalized Tate cohomology (2005, unknown): “If Gorproj $ dimM<\infty$ then $Ext_{g}^{i}(M, N)\simeq Ext_{\ovalbox{\tt\small REJECT} J}^{i}(M, N)$ for any $i\geq 0$ ([4], Theorem 3.”
Gorenstein Homological Algebra of Artin Algebras (2017, methodology): “Gorenstein derived functors are then defined using a Gorenstein-projective resolution of a module ([28, 36]).”