For the simplest inflation models, the recent detection of a large primordial B-mode polarization signal by the BICEP2 experiment indicates a slight tension with the upper limit on the tensor-to-scalar ratio, r, from the Planck satellite. Here, we discuss spatially varying r as a possible explanation for this discrepancy. This idea seems attractive since it may also explain part of the hemispherical temperature power asymmetry seen by Wilkinson Microwave Anisotropy Probe and Planck at large angular scales. If these two aspects are indeed connected, the model suggests that in the Northern hemisphere r should be much smaller, a hypothesis that could be confirmed with future B-mode experiments, providing a test for the stationarity of primordial tensor contributions across the sky. The BICEP2 measurement furthermore rules out that a simple dipolar modulation of r alone can be responsible for the full hemispherical power asymmetry.