  We introduce a notion of shadowing property for actions of finitely generated
groups and study its basic properties. We formulate and prove a shadowing lemma
for actions of nilpotent groups. We construct an example of a faithful linear
action of a solvable Baumslag-Solitar group and show that the shadowing
property depends on quantitative characteristics of hyperbolicity. Finally we
show that any linear action of a non-abelian free group does not have the
shadowing property.
