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A content-matched (CM) rangemonitoring query overmoving objects continually retrieves the moving objects (i) whose non-spatial attribute values are matched to given non-spatial query values; and (ii) that are currently located within a given spatial query range. In this paper, we propose a new query indexing structure, called the group-aware query region tree (GQR-tree) for efficient evaluation of CMrange monitoring queries. The primary role of the GQR-tree is to help the server leverage the computational capabilities of moving objects in order to improve the system performance in terms of the wireless communication cost and server workload. Through a series of comprehensive simulations, we verify the superiority of the GQR-tree method over the existing methods.