  In this paper, we show that the semi-Dirichlet C*-covers of a semi-Dirichlet
operator algebra form a complete lattice, establishing that there is a maximal
semi-Dirichlet C*-cover. Given an operator algebra dynamical system we prove a
dilation theory that shows that the full crossed product is isomorphic to the
relative full crossed product with respect to this maximal semi-Dirichlet
cover. In this way, we can show that every semi-Dirichlet dynamical system has
a semi-Dirichlet full crossed product.
