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Digital Twin (DT) technology is far from being comprehensive and mature, resulting in their piecemeal implementation in practice where some functions are automated by DTs, and others are still performed by humans. This piecemeal implementation of DTs often leaves practitioners wondering what roles (or functions) to allocate to DTs in a work system, and how might it impact humans. A lack of knowledge about the roles that humans and DTs play in a work system can result in significant costs, misallocation of resources, unrealistic expectations from DTs, and strategic misalignments. To alleviate this challenge, this paper answers the research question: When humans work with DTs, what types of roles can a DT play, and to what extent can those roles be automated? Specifically, we propose a two-dimensional conceptual framework, Levels of Digital Twin (LoDT). The framework is an integration of the types of roles a DT can play, broadly categorized under (1) Observer, (2) Analyst, (3) Decision Maker, and (4) Action Executor, and the extent of automation for each of these roles, divided into five different levels ranging from completely manual to fully automated. A particular DT can play any number of roles at varying levels. The framework can help practitioners systematically plan DT deployments, clearly communicate goals and deliverables, and lay out a strategic vision. A case study illustrates the usefulness of the framework. • Digital Twin human interaction • Digital Twin can play multiple roles in a work system. • Levels of Digital Twin framework provides a common language for understanding. • Digital Twin must be evaluated for each case – a "one size fits all" does not work. [ABSTRACT FROM AUTHOR]