Induced modules for vertex operator algebras

For a vertex operator algebra $V$ and a vertex operator subalgebra $V'$ which is invarinant under an automorphism $g$ of $V$ of finite order, we introduce a $g$-twisted induction functor from the category of $g$-twisted $V'$-modules to the category of $g$-twisted $V$-modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated with $V$ being simple or with $V'$ being $g$-rational.