  In this paper we develop a formalism for working with twisted realizations of
vertex and conformal algebras. As an example, we study realizations of
conformal algebras by twisted formal power series. The main application of our
technique is the construction of a very large family of representations for the
vertex superalgebra $\goth V_\Lambda$ corresponding to an integer lattice
$\Lambda$. For an automorphism $\^\sigma:\goth V_\Lambda\to\goth V_\Lambda$
coming from a finite order automorphism $\sigma:\Lambda \to \Lambda$ we define
a category $\cal O_{\^\sigma}$ of twisted representations of $\goth V_\Lambda$
and show that this category is semisimple with finitely many isomorphism
classes of simple objects.
