We observe, with angle-resolved photoemission, a dramatic change in the electronic structure of two C60 monolayers, deposited, respectively, on Ag (111) and (100) substrates, and similarly doped with potassium to half filling of the C60 lowest unoccupied molecular orbital. The Fermi surface symmetry, the bandwidth, and the curvature of the dispersion at Gamma point are different. Orientations of the C60 molecules on the two substrates are known to be the main structural difference between the two monolayers, and we present new band-structure calculations for some of these orientations. We conclude that orientations play a key role in the electronic structure of fullerides.