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We consider a Peer-to-Peer (P2P) data sharing setting in wireless mesh networks (WMNs), wherein few mesh routers are provisioned with storage capacity and act as caches and participants in the P2P content sharing. Our contributions in this paper are optimum replication strategies for the P2P objects at the participating mesh routers to reduce the communication cost between peers within the WMN. We determine the optimum number of replicas for each object such that the average access cost of all objects in the network is minimized. We then propose a distributed algorithm for object replication and show that the distributed algorithm mimics the optimal strategy very well. The simulation results show that our strategy reduces the communication cost as compared to other commonly used strategies by a ratio of ≈20%.