(G,?)-equivariant ?-coordinated quasi modules for nonlocal vertex algebras

In this paper, we study $(G,\chi_{\phi})$-equivariant $\phi$-coordinated quasi modules for nonlocal vertex algebras. Among the main results, establish several conceptual including a generalized commutator formula and general construction of weak quantum algebras their modules. As an application, also construct (equivariant) lattice by using Lepowsky's work on twisted operators.