  We study some graded geometric constructions appearing naturally in the
context of gauge theories. Inspired by a known relation of gauging with
equivariant cohomology we generalize the latter notion to the case of arbitrary
Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using
this concept we describe a procedure for analysis of gauge symmetries of given
functionals as well as for constructing functionals (sigma models) invariant
under an action of some gauge group.
  As the main example of application of these constructions we consider the
twisted Poisson sigma model. We obtain it by a gauging-type procedure of the
action of an essentially infinite dimensional group and describe its symmetries
in terms of classical differential geometry.
  We comment on other possible applications of the described concept including
the analysis of supersymmetric gauge theories and higher structures.
