How does work function transform in Einstein's special theory of relativity? A photon with energy greater than the work function hits the metal, and an electron is knocked off.
Now, suppose we were in an inertial frame moving with a velocity $v$ with respect to the metal such that the photon is red-shifted to have an energy less than the work function. Will we observe the electron being knocked off now?
The knocking off of an electron is a physical phenomenon and must occur in all frames, if in one.
 A: 
How does work function transform in Einstein's special theory of relativity?

The work function of (some particular spot on the surface of) some particular piece of metal is not subject to transformation at all;
instead it is a proper attribute of this piece of metal under consideration;    it remains invariant under any (change of) description.

A photon with energy greater than the work function hits the metal, and an electron is knocked off.

Likewise, the energy of a particular photon with respect to the particular piece of metal under consideration (necessarily, before the electron was knocked off and the remaining piece of metal might have picked up some momentum with respect to the (inertial) reference system to which it had belonged initially) is an invariant;
its value is independent of the choice of (inertial) reference system with respect to which the photon and the piece of metal might be described.

Now, suppose we were in an inertial frame moving with a velocity v with respect to the metal such that the photon is red-shifted to have an energy less than the work function. 

The photon would consequently be (described as) red-shifted with respect to (the members of) this additionally introduced inertial frame;
but of course not with respect to the piece of metal under consideration.
The energy of this photon with respect to (members of) this additionally introduced inertial frame would be lower by a factor $$\sqrt{\frac{1 - \left(\frac{v}{c}\right)^2}{1 + \left(\frac{v}{c}\right)^2}}$$ compared to the energy of this photon with respect to the piece of metal.
(It's just improper to attribute a value of energy e.g. to a photon without specifying with respect to which (suitable) reference system the energy is meant to be evaluated.) 
