  We model and analyse the secular evolution of stellar bars in spinning dark
matter (DM) haloes with the cosmological spin lambda ~ 0 -- 0.09. Using
high-resolution stellar and DM numerical simulations, we focus on angular
momentum exchange between stellar discs and DM haloes of various axisymmetric
shapes --- spherical, oblate and prolate. We find that stellar bars experience
a diverse evolution which is guided by the ability of parent haloes to absorb
angular momentum lost by the disc through the action of gravitational torques,
resonant and non-resonant. We confirm the previous claim that dynamical bar
instability is accelerated via resonant angular momentum transfer to the halo.
Our main findings relate to the long-term, secular evolution of disc-halo
systems: with an increasing lambda, bars experience less growth and dissolve
after they pass through the vertical buckling instability. Specifically, with
an increasing halo spin, (1) The vertical buckling instability in stellar bars
colludes with inability of the inner halo to absorb angular momentum --- this
emerges as the main factor weakening or destroying bars in spinning haloes; (2)
Bars lose progressively less angular momentum, and their pattern speeds level
off; (3) Bars are smaller, and for lambda >= 0.06 cease their growth completely
following buckling; (4) Bars in lambda > 0.03 haloes have ratio of
corotation-to-bar radii, R_CR / R_b > 2, and represent so-called slow bars
which do not show offset dust lanes. We provide a quantitative analysis of
angular momentum transfer in disc-halo systems, and explain the reasons for
absence of growth in fast spinning haloes and its observational corollaries. We
conclude that stellar bar evolution is substantially more complex than
anticipated, and bars are not as resilient as has been considered so far.
