A microscopic theory is developed for the projection (quantum mirage) of the Kondo resonance from one focus of an elliptic quantum corral to the other focus. The quantum mirage is shown to be independent of the size and the shape of the ellipse, and experiences lambda (F)/4 oscillations (lambda (F) is the surface-band Fermi wavelength) with an increasing semimajor axis length. We predict an oscillatory behavior of the mirage as a function of a weak magnetic field applied perpendicular to the sample.