  Recent experimental data have demonstrated that $^{76}$Ge may be a rare
example of a nucleus exhibiting rigid $\gamma$-deformation in the low-spin
regime. In the present work, the experimental analysis is supported by
microscopic calculations using the multi-quasiparticle triaxial projected shell
model (TPSM) approach. It is shown that to best describe the data of both yrast
and $\gamma$-vibrational bands in $^{76}$Ge, a rigid-triaxial deformation
parameter $\gamma\approx 30^\circ$ is required. TPSM calculations are discussed
in conjunction with the experimental observations and also with the published
results from the spherical shell model. The occurrence of a $\gamma\gamma$-band
in $^{76}$Ge is predicted with the bandhead at an excitation energy of $ \sim$
2.5 MeV. We have also performed TPSM study for the neighboring Ge- and
Se-isotopes and the distinct $\gamma$-soft feature in these nuclei is shown to
result from configuration mixing of the ground-state with multi-quasiparticle
states.
