Context : The orbital obliquity of planets with respect to the rotational axis of their host stars is a relevant parameter for the characterization of the global architecture of planetary systems and a key observational constraint to discriminate between different scenarios proposed to explain the existence of close-in giant planets . Aims : In the framework of the GAPS project , we are conducting an observational programme aimed at the determination of the orbital obliquity of known transiting exoplanets . The targets are selected to probe the obliquity against a wide range of stellar and planetary physical parameters . Methods : We exploit high-precision radial velocity ( RV ) measurements , delivered by the HARPS-N spectrograph at the 3.6m Telescopio Nazionale Galileo , to measure the Rossiter-McLaughlin ( RM ) effect in RV time-series bracketing planet transits , and to refine the orbital parameters determinations with out-of-transit RV data . We also analyse new transit light curves obtained with several 1-2m class telescopes to better constrain the physical fundamental parameters of the planets and parent stars . Results : We report here on new transit spectroscopic observations for three very massive close-in giant planets : WASP-43 b , HAT-P-20 b and Qatar-2 b ( M _ { p } = 2.00 , 7.22 , 2.62 M _ { J } ; a = 0.015 , 0.036 , 0.022 AU , respectively ) orbiting dwarf K-type stars with effective temperature well below 5000 K ( T _ { eff } = 4500 \pm 100 , 4595 \pm 45 , 4640 \pm 65 K respectively ) . These are the coolest stars ( except for WASP-80 ) for which the RM effect has been observed so far . We find \lambda = 3.5 \pm 6.8 deg for WASP-43 b and \lambda = -8.0 \pm 6.9 deg for HAT-P-20 b , while for Qatar-2 , our faintest target , the RM effect is only marginally detected , though our best-fit value \lambda = 15 \pm 20 deg is in agreement with a previous determination . In combination with stellar rotational periods derived photometrically , we estimate the true spin-orbit angle , finding that WASP-43 b is aligned while the orbit of HAT-P-20 b presents a small but significant obliquity ( \varPsi =36 _ { -12 } ^ { +10 } deg ) . By analyzing the CaII H & K chromospheric emission lines for HAT-P-20 and WASP-43 , we find evidence for an enhanced level of stellar activity which is possibly induced by star-planet interactions . Conclusions :