Does the Cosmic Microwave Background falsify relativity of velocity? In special relativity velocity is relative and there is no absolute rest frame . However the cosmic microwave background radiation does have a rest frame. Earth is moving with 328 km/s with respect to this frame, on average, and the local group with 627 km/s. It is plausible that this remnant of the big bang represents the rest frame of all matter in the universe. The question is therefore: does the CMB falsify the tenet of SRT that velocity is relative ? Or should we see all matter in the universe, minus Earth, as just another object moving in space ? 
 A: This questions turns on a focus on words over the physics they are suppose to describe.
Special relativity says that physics (including Maxwell's equations) is the same in every inertial frame. The word "absolute" is a distraction from the important principle about physics.
Sure the CMB has a local rest frame. So what? Everything has a rest frame (even accelerating objects have a momentarily co-moving frame). 
Those things are identifiable frames. They are not absolute in the sense that physics is different for those frame than for any other.
A: 
However the cosmic microwave background radiation does have a rest frame. 

All particles in an ensemble  with their $(E,p_x,p_y,p_z)$ vectors can be transformed to an inertial frame where the summed  momentum is zero, a rest frame. For zero mass particles at least two non collinear ones are needed for a definition consistent with special relativity ( a zero mass particle has no rest frame, ). 
So , yes, one studies the CMB in its rest mass system, against which the motion  of the earth has been detected as a distortion to the hypothesis that the CMB  and the earth are at the same rest frame.

It is plausible that this remnant of the big bang represents the rest frame of all matter in the universe. 

Not in mainstream physics models where special and general relativity are absolutely obeyed. There is no evidence other your hypothesis, but special relativity is continuously validated by all experiments and observations.
The $π_0$ has a rest frame, and it decays to two photons. In an event it is not in its rest frame, the photons have to be transformed to the total event rest frame. In no way can one say that the rest frame of the $π_0$ is an absolute frame ( or of any other particle in the event). One has the Lorentz transformations to go from one relative rest frame to another, and the same will be true for the CMB rest frame if it becomes necessary for some research purpose ( as when  deriving the velocity of the earth from the dipole distortions which show that the measurements are not done in the rest frame of the CMB).
