Globally, there is a tremendous growth in mobile data traffic and mobile network operators (MNO) are investing heavily to expand and operate their networks to serve them. The operational expenditure incurred by MNOs are increasing much more compared to revenue from mobile data traffic, thereby decreasing their profit margins. One of the major components of operational expenditure is the cost of operating cellular base stations using grid power or diesel generators in the absence of grid power. MNOs in off-grid sites constantly rely on diesel generators to run base stations that is very expensive. At the same time, they also cause adverse environmental impact due to CO2 emission. While the economics of renewable energy are already favorable in remote off-grid areas, it has been quite challenging for operators to handle the unpredictability of renewable energy sources while meeting the user QoE. In this work, we present GreenSlice, an 'energy-source' aware asynchronous content delivery mechanism that adapts delivery of bulk delay-tolerant content in periods of availability of renewable energy. In particular, given a set of heavy demands (such as downloads of videos, software updates etc.), we present a scheduling algorithm that balances the operator's energy cost and delay experienced by users. We use a novel adaptation of Lyapunov optimization framework to provide bounds on the content delivery time and resulting operational cost. Simulation studies show our mechanism reduces the energy cost by more than 33% compared to traditional schemes of using renewables and non-renewables without asynchronous content delivery, at the same time keeping the increase in delay negligible. © 2014 IEEE.