Room temperature electron mobility of 1170 cm(2)/V s is obtained in an undoped, lattice-matched, Al0.82In0.18N/GaN field-effect transistor heterostructure, while keeping a high (2.6 +/- 0.3)x10(13) cm(-2) electron gas density intrinsic to the Al0.82In0.18N/GaN material system. This results in a two-dimensional sheet resistance of 210 Omega/square. The high mobility of these layers, grown by metal-organic vapor phase epitaxy on sapphire substrate, is obtained thanks to the insertion of an optimized AlN interlayer, reducing the alloy related interface roughness scattering. (c) 2006 American Institute of Physics.