Using angle-resolved photoemission spectroscopy, we have investigated changes in the band dispersion of a free-electron-like surface state of Si(111)-√3×√3-Ag, induced by adsorption of submonolayer Au adatoms. At room temperature, where the adatoms are in a two-dimensional adatom-gas phase, electrons are transferred from the Au adatoms to the substrate, shifting the surface band downwards and increasing the band occupation (carrier doping), and also causing it to deviate from a parabolic dispersion. At 135 K where the Au adatoms are frozen at specific sites of the substrate, the surface-state band splits into two. This is the first experimental verification of band splitting that can be explained in terms of hybridization between the unperturbed surface-state band and the localized virtual bound states induced by the adatoms. This kind of interaction between localized states around individual impurity atoms and extended carriers are very important and common in various physical phenomena such as Kondo effect and diluted magnetic semiconductors.