It is notorious that, contrary to all other precision electroweak data, the forward-backward asymmetry for b quarks $A_{FB}^b$ measured in Z decays at LEP1 is nearly three standard deviations away from the predicted value in the Standard Model; significant deviations also occur in measurements of the asymmetry off the Z pole. We show that these discrepancies can be resolved in a variant of the Randall-Sundrum extra-dimensional model in which the gauge structure is extended to $SU(2)_L times SU(2)_R times U(1)_X$ to allow for relatively light Kaluza-Klein excitations of the gauge bosons. In this scenario, the fermions are localized differently along the extra dimension, in order to generate the fermion mass hierarchies, so that the electroweak interactions for the heavy third generation fermions are naturally different from the light fermion ones. We show that the mixing between the Z boson with the Kaluza-Klein excitations allows to explain the $A_{FB}^b$ anomaly without affecting (and even improving) the agreement of the other precision observables, including the $Z to bb$ partial decay width, with experimental data. Some implications of this scenario for the ILC are summarized.
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