It is widely believed that the cosmological redshift is not a Doppler shift .
However , Bunn & Hogg have recently pointed out that to settle properly this problem , one has to transport parallely the velocity four-vector of a distant galaxy to the observer ’ s position .
Performing such a transport along the null geodesic of photons arriving from the galaxy , they found that the cosmological redshift is purely kinematic .
Here we argue that one should rather transport the velocity four-vector along the geodesic connecting the points of intersection of the world-lines of the galaxy and the observer with the hypersurface of constant cosmic time .
We find that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula .
Instead , for small redshifts it coincides with the well known non-relativistic decomposition of the redshift into a Doppler ( kinematic ) component and a gravitational one .
We perform such a decomposition for arbitrary large redshifts and derive a formula for the kinematic component of the cosmological redshift , valid for any FLRW cosmology .
In particular , in a universe with \Omega _ { \mathrm { m } } = 0.24 and \Omega _ { \Lambda } = 0.76 , a quasar at a redshift 6 , at the time of emission of photons reaching us today had the recession velocity v = 0.997 c .
This can be contrasted with v = 0.96 c , had the redshift been entirely kinematic .
Thus , for recession velocities of such high-redshift sources , the effect of deceleration of the early Universe clearly prevails over the effect of its relatively recent acceleration .
Last but not least , we show that the so-called proper recession velocities of galaxies , commonly used in cosmology , are in fact radial components of the galaxies ’ four-velocity vectors .
As such , they can indeed attain superluminal values , but should not be regarded as real velocities .