- classical (Maxwell): electrons in the medium oscillate out of phase in response to the incident wave; this results in a new wave, propagating somewhat slower

- quantum (QED): incident photon couples to matter excitation (an exciton), producing a pseudo-particle called a polariton; it has a non-zero effective mass, resulting in propagation slower than c

As mentioned above, it absolutely isn't "absorbing and re-emitting". If that was the case, transparent materials would not exist (only milky/clouded ones), as re-emission is in random direction. However, photon propagation in the Sun is just that, a (very long, counting from the core to photosphere) random walk.