Peer-to-Peer (P2P) networks have been proposed as a promising approach to create more scalable Networked Virtual Environment (NVE) systems, but P2P-NVE also increases the probability of cheating by allowing users to manage the states of objects. In this paper, we propose Delaunay State Management (DSM), a P2P-NVE state management scheme that divides the whole virtual world into many triangular regions by Delaunay triangulation. In DSM, each region is managed by three super-peers, whose collective decisions determine how states will change. Assuming that at most one of the three super-peers is malicious, effective anti-cheating can be provided. Additionally, we also describe how DSM provides essential state management functions (e.g., consistency, load-balancing, and faulttolerance), and conclude with its potential applications.