  The structure of even-even neutron-rich Ru, Mo, Zr and Sr nuclei in the
$A\approx 100$ mass region is studied within the interacting boson model (IBM)
with microscopic input from the self-consistent mean-field approximation based
on the Gogny-D1M energy density functional. The deformation energy surface in
the quadrupole deformation space $(\beta,\gamma)$, computed within the
constrained Hartree-Fock-Bogoliubov framework, is mapped onto the expectation
value of the appropriately chosen IBM Hamiltonian with configuration mixing in
the boson condensate state. The mapped IBM Hamiltonian is used to study the
spectroscopic properties of $^{98-114}$Ru, $^{96-112}$Mo, $^{94-110}$Zr and
$^{92-108}$Sr. Several cases of $\gamma$-soft behavior are predicted in Ru and
Mo nuclei while a pronounced coexistence between strongly-prolate and
weakly-oblate deformed shapes is found for Zr and Sr nuclei. The method
describes well the evolution of experimental yrast and non-yrast states as well
as selected $B$(E2) transition probabilities.
