Killing of supports on graded algebras

Killing of supports along subsets of a group G and regradings along certain maps of groups are studied, in the context of group-graded algebras. We show that, under precise conditions on and φ, the module theories over the initial and the final algebras are functorially well-connected. Special attention is paid to G=Z, in which case the results can be applied to n-Koszul algebras.