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This paper develops the orbifold theory for $\\mathbb{C}[\\J Z]$. A finite-order linear automorphism $g$ of $Z$ acts by vertex algebra automorphisms on $\\mathbb{C}[\\J Z]$. We show that $\\mathbb{C}[\\J^g Z]$, where $\\J^g Z$ is the scheme of $g$--twisted jets has the structure of a $g$-twisted $\\mathbb{C}[\\J Z]$ module. 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