High-spin states in 3676Kr40 have been populated in the 40Ca(40Ca,4p)76Kr fusion-evaporation reaction at a beam energy of 165 MeV, and studied using the GAMMASPHERE and MICROBALL multi-detector arrays. The ground-state band and two signature-split negative-parity bands of 76Kr have been extended to ∼30hℏ. Lifetime measurements using the Doppler-shift attenuation method indicate that the transition quadrupole moment of these three bands decrease as they approach their maximum-spin states.