As the growth of mobile video traffic outpaces that of cellular network speed, industry is adopting HTTP-based adaptive video streaming technology which enables dynamic adaptation of video bit-rates to match changing network conditions. However, recent measurement studies have observed problems in fairness, stability, and efficiency of resource utilization when multiple adaptive video flows compete for bandwidth on a shared wired link. Through ex- periments and simulations, we confirm that such undesirable be- havior manifests itself in cellular networks as well. To overcome these problems, we design an in-network resource management framework, AVIS, that schedules HTTP-based adaptive video flows on cellular networks. AVIS effectively manages the resources of a cellular base station across adaptive video flows. AVIS also pro- vides a framework for mobile operators to achieve a desired bal- Ance between optimal resource allocation and user quality of expe- rience. AVIS has three key differentiating features: (1) It optimally computes the bit-rate allocation for each user, (2) It includes a scheduler and per-flow shapers to enforce bit-rate stability of each flow and (3) It leverages the resource virtualization technique to separate resource management of adaptive video flows from reg- ular video flows. We implement a prototype system of AVIS and evaluate it on both a WiMAX network testbed and a LTE system simulator to show its efficacy and scalability.