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Wireless spectrum is a scare resource, but in practice much of it is underused by current owners. To enable better use of this spectrum, we propose an auction approach that leverages dynamic spectrum access techniques to allocate spectrum in a secondary market. These are markets where spectrum owners can either sell or lease spectrum to other parties. Unlike previous auction approaches, we seek to take advantage of the ability to share spectrum among some bidders while respecting the needs of others for exclusive use. Thus, unlike unlicensed spectrum (e.g., Wi-Fi), which can be shared by any device, and exclusive-use licensed spectrum, where sharing is precluded, we enable efficient allocation by supporting sharing alongside quality-of-service protections. We present SATYA (Sanskrit for "truth"), a strategyproof and scalable spectrum auction algorithm whose primary contribution is in the allocation of a right to contend for spectrum to both sharers and exclusive-use bidders. Achieving strategyproofness in our setting requires appropriate handling of the externalities created by sharing. Using realistic Longley-Rice-based propagation modeling and data from the FCC's CDBS database, we conduct extensive simulations that demonstrate SATYA's ability to handle heterogeneous agent types involving different transmit powers and spectrum needs.