Complex event detection over data streams has become ubiquitous through the widespread use of sensors, wireless connectivity and the wide variety of end-user mobile devices. Typically, such event detection is carried out by a data stream management system executing continuous queries (CQs), registered by the users. In this paper, we consider the situation where the results of the CQs, which are in the form of individual data streams, are disseminated to the users' hand-held, battery-operated devices over a shared broadcast medium. In order to reduce the overall energy consumption of the mobile devices, we propose Bose*, a power-aware query operator placement algorithm that determines which part of a CQ plan should be executed at the data stream management system and which part should be executed at the mobile device. Bose*'s effectiveness in reducing energy consumption, as well as response time under specific conditions, is evaluated using simulation, driven by parameters measured on real mobile devices.