LetRbe a commutative ringGa free abelian group of finite ranknandR#Gthe corresponding skew group ring. We fix an integerm; 0 ≤m≤nand a free subgroupGmofGof rankm. We prove that ifRis noetherian, ifspecG(R#Gm) is (R,G)-normally separated and if the Laurent polynomial ringis catenary, then the ringR#GmisG-catenary. In the particular case whereRis an affine algebra over an algebraically closed field, we prove that ifRisG-locally finite, then the skew group ringR#Gmis universally catenary and universallyG-catenary. Furthermore Tauvel's height formula is valid in all prime factors andG-prime factors ofR#Gm.