Peer-to-peer (P2P) architectures have recently become a popular design choice to build scalable Networked Virtual Environments (NVEs). While P2P architectures offer better scalability than server-based architectures, efficient distribution and management of avatar and object states remains a highly challenging issue. In this paper, we propose GROUP, a fully-distributed P2P architecture for NVEs that addresses this issue by combining a structured P2P overlay, used for object state management, with a Voronoi-based overlay, used for avatar state and group membership management. The resulting dual overlay architecture enables efficient and fully distributed management of state updates for P2P-based NVEs.