Yes, the Sun does undergo a process that involves the transformation of matter. The primary process responsible for the Sun's energy production is nuclear fusion. In the core of the Sun, under the extreme conditions of high temperature and pressure, hydrogen nuclei (protons) combine to form helium nuclei through a series of fusion reactions.
The most common fusion reaction in the Sun, known as the proton-proton chain, involves four hydrogen nuclei fusing to create a helium nucleus. This process releases a tremendous amount of energy in the form of light and heat. The mass of the resulting helium nucleus is slightly less than the combined mass of the four original hydrogen nuclei. This difference in mass is converted into energy according to Einstein's famous equation, E=mc².
In this way, the Sun transforms matter by converting a small fraction of its mass into energy through the process of nuclear fusion. This continuous release of energy from the Sun's core is what powers its radiation and provides heat and light to the solar system.