THE PICARD GROUP OF A CATEGORY OF GRADED MODULES

For R a G-graded ring, we study Pic(R-gr), the group of isomorphism cl asses of autoequivalences of the category of graded left R-modules. Fo r G infinite, this requires generalizing the classical sequences invol ving Pic(A), A a k-algebra, to A a ring with local units. Then for G e ither finite or infinite, we characterize the inner automorphisms in s ome subgroups H of the automorphism group of the smash product R#P-G a nd thus obtain some subgroups of Pic(R-gr).