We report numerical investigation of several effects accompanying propagation of femtosecond pulses in air-core photonic crystal fibers.We have found that the strong Raman response of air does not always result in the large soliton self-frequency shift, because it can simultaneously stimulate energy losses into non-solitonic radiation. We demonstrate that the pronounced spectral tails seen in many recent experiments on the short wavelength side of the soliton spectra can be associated with emission of Airy waves by the decelerating solitons. For pulse durations close to 10fs all radiation effects due to Raman response of air become negligible for a special choice of the peak power leading to propagation in the self-induced transparency regime.