We extend Schwede's work on the unstable global homotopy theory of orthogonal spaces and L-spaces to the category of *-modules (i.e., unstable S-modules). We prove a theorem which transports model structures and their properties from L-spaces to *-modules and show that the resulting global model structure for *-modules is monoidally Quillen equivalent to that of orthogonal spaces. As a consequence, there are induced Quillen equivalences between the associated model categories of monoids, which

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... dentify equivalent models for the global homotopy theory of A_∞-spaces.