This paper describes properties and behavior of magnetic reconnection and flux transfer events (FTE) on the dayside magnetopause using the global hybrid‐Vlasov code Vlasiator. We investigate two simulation runs with and without a sunward (positive) Bх component of the interplanetary magnetic field (IMF) when the IMF is southward. The runs are two‐dimensional in real space in the noon‐midnight meridional (polar) plane and three‐dimensional in velocity space. Solar wind input parameters are identical in the two simulations with the exception that the IMF is purely southward in one but tilted 45° towards the Sun in the other. In the purely southward case (i.e., without Bх) the magnitude of the magnetosheath magnetic field component tangential to the magnetopause is larger than in the run with a sunward tilt. This is because the shock normal is perpendicular to the IMF at the equatorial plane, whereas in the other run the shock configuration is oblique and a smaller fraction of the total IMF strength is compressed at the shock crossing. Hence the measured average and maximum reconnection rate are larger in the purely southward run. The run with tilted IMF also exhibits a north‐south asymmetry in the tangential magnetic field caused by the different angle between the IMF and the bow shock normal north and south of the equator. Greater north‐south asymmetries are seen in the FTE occurrence rate, size, and velocity as well; FTEs moving towards the southern hemisphere are larger in size and observed less frequently than FTEs in the northern hemisphere.