  In the present paper we continue the study of the structure of a Banach
algebra B(A, T_g) generated by a certain Banach algebra $A$ of operators acting
in a Banach space $D$ and a group {T_g}_{g \in G} of isometries of D such that
T_g A T^{-1}_g = A. We investigate the interrelations between the existence of
the expectation of B(A, T_g) onto $A$, metrical freedom of the automorphisms of
A induced by T_g and the dual action of the group G on B(A, T_g). The results
obtained are applied to the description of the structure of Banach algebras
generated by 'weighted composition operators' acting in Lebesgue spaces.
