Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear if and only if G is a finitely generated virtually nilpotent group.
OLSHANSKII, A. YU. (2007) "Linear Automorphism Groups of Relatively Free Groups," Turkish Journal of Mathematics: Vol. 31: No. 5, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol31/iss5/8