  We study the spectrum of bosonic string theory on rotating BTZ black holes,
using a SL(2,R) WZW model. Previously, Natsuume and Satoh have analyzed strings
on BTZ black holes using orbifold techniques. We show how an appropriate
spectral flow in the WZW model can be used to generate the twisted sectors,
emphasizing how the spectral flow works in the hyperbolic basis natural for the
BTZ black hole. We discuss the projection condition which leads to the
quantization condition for the allowed quantum numbers for the string
excitations, and its connection to the anomaly in the corresponding conserved
Noether current.
