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A detailed study of charge transport in the paramagnetic phase of the cage-cluster dodecaboride Ho0.8Lu0.2B12 with an instability both of the fcc lattice (cooperative Jahn–Teller effect) and the electronic structure (dynamic charge stripes) was carried out at temperatures 1.9–300 K in magnetic fields up to 80 kOe. Four mono-domain single crystals of Ho0.8Lu0.2B12 samples with different crystal axis orientation were investigated in order to establish the singularities of Hall effect, which develop due to (i) the electronic phase separation (stripes) and (ii) formation of the disordered cage-glass state below T*~60 K. It was demonstrated that a considerable intrinsic anisotropic positive component ρanxy appears at low temperatures in addition to the ordinary negative Hall resistivity contribution in magnetic fields above 40 kOe applied along the [001] and [110] axes. A relation between anomalous components of the resistivity tensor ρanxy~ρanxx1.7 was found for H||[001] below T*~60 K, and a power law ρanxy~ρanxx0.83 for the orientation H||[110] at temperatures T < TS~15 K. It is argued that below characteristic temperature TS~15 K the anomalous odd ρanxy(T) and even ρanxx(T) parts of the resistivity tensor may be interpreted in terms of formation of long chains in the filamentary structure of fluctuating charges (stripes). We assume that these ρanxy(H||[001]) and ρanxy(H||[110]) components represent the intrinsic (Berry phase contribution) and extrinsic (skew scattering) mechanism, respectively. Apart from them, an additional ferromagnetic contribution to both isotropic and anisotropic components in the Hall signal was registered and attributed to the effect of magnetic polarization of 5d states (ferromagnetic nano-domains) in the conduction band of Ho0.8Lu0.2B12.