The development of the Kelvin-Helmholtz instability (KHI) in a purely transverse geometry (velocity shear perpendicular to the magnetic field), simulated using the hybrid-Vlasov model Vlasiator. The parameters shown are: Proton temperature (panel a), the non-Maxwellianity of the proton velocity distribution function (panel b), proton heat flux (panel c) and vorticity (panel d). A black contour in each panel shows the region where the magnitude of the proton temperature gradient is larger than the maximum gradient at the beginning of the simulation. Arrows in panel d) show the velocity field. The evolution of KHI proceeds from the formation of linear surface waves (t<50 Ωc,p-1) to the waves rolling up into vortices (t>50 Ωc,p-1). Due to the steepening of the velocity shear layer, whose thickness tends towards the thermal proton Larmor radius, finite Larmor radius effects become active at the vortex edges, manifesting as enhanced non-Maxwellianity (panel b) and a heat flux (panel c), which originates from the temperature gradient according to the mechanism described by Braginskii (1965). At the end of the simulation (t=90-100 Ωp-1), non-Maxwellianity increases also in the vortex interior, as protons from the two initial regions are mixed together.