2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113987For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f:X->X. Under mild hypotheses, these lower bounds are sharp. We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic to a fixed point free G-map if the generalized equivariant Lefschetz invariant of f is zero. Finally, we prove a converse of the equivariant Lefschetz fixed point theorem.17 pages, submitted to Pacific Journal of MathematicsAlgebraic Topology55M20, 57R91 (Primary); 54H25, 57S99 (Secondary)text