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The high frequency segment (10-66 GHz) of the IEEE 802.16 standard seems promising for the implementation of wireless backhaul networks carrying large volumes of Internet traffic. In contrast to wireline backbone networks, where channel errors seldom occur, routing decisions in IEEE 802.16 networks are conditioned by wireless channel impairments rather than by congestion, exclusively. This renders a cross-layer routing approach between the routing and the physical layers more appropriate during fading periods. In this paper, an adaptive cross-layer routing scheme is presented based on the selection of the most reliable path in terms of packet error ratio (unipath routing). The paper argues that routing Internet traffic through wireless backhaul networks is modeled more realistically employing evolutionary rather than conventional game theory. The stability of the proposed routing algorithm is proven and the dependence of the speed of convergence on various physical layer parameters is investigated. Is is also shown that convergence may be further accelerated by increasing the amount of information from the physical layer, specifically the physical separation between the alternative paths provided to the routing layer.