In this paper, we propose a green backhaul infrastructure virtualization market for a renewable-powered cellular multi-hop backhaul network in which a virtual operator (VO) can use the backhaul networks of some assemble operators (AOs) to forward traffic to itself. In particular, some backhaul nodes (i.e., on-grid nodes) of each assemble operator are considered to be powered by renewable energy suppliers (RPSs). In response to stochastic traffic demand, the virtual operator sets traffic service prices it will pay to the assemble operators, and the assemble operators set energy prices they will pay to the RPSs. In addition, each AO should determine the amount of renewable energy that will be reserved for the off-grid node, and each RPS should determine how much energy should be stored. This paper explicitly characterizes the equilibrium price and resource coordination strategies for such a mulit-stage resource virtualization market, so that the decentralized system can operates in a stable and efficient way. Based on that, we derive results regarding higher-level integrated backhaul structural choices by the virtual operator, such as whether it sets up the backhaul network independently or uses the integrated backhaul network and which operators to choose as assemble operators. A novel algorithm is developed to find the sequential equilibrium solution that can properly cope with these peer effects. The simulation results show that the proposed integrated green multi-hop backhaul system yields substantial gains for both operators and renewable energy suppliers compared with a non-virtualization backhaul network using conventional energy. The results also provide insights on how to manage cellular backhaul virtualization pricing and the cost of renewable energy for the design of green dense small cell networks in future mobile networks.