Stellar population synthesis models are crucial for the understanding of the large amount of data which is being gathered for galaxies at low and high redshift, and provide the only way to compare the ``real world'' with the theoretical framework. The best models require extensive empirical stellar spectral libraries, which at present are starting to be quite complete in the optical range. However the situation is different in the near-infrared, which observational windows have been, until recently, poorly exploited. This is specially due to the lack of appropriate instrumentation. We present the preliminary results of an ongoing observational program aimed to overcome this problem and to provide a stellar library in the K band with the required coverage of physical stellar parameters: effective temperature, gravity, metallicity and non-solar abundance ratios. In particular, the CO feature at 2.3 μ m is a very promising spectroscopic line-strength index that will help to face outstanding problems in galaxy formation and evolution. The availability of this library will be essential to interpret the stellar content of composite stellar populations with EMIR. In addition, this library will be also useful for other purposes, like the study of highly reddened objects, and the spectral classification of late type stars.