gamma matrices out of pauli matrices - symmetry/group theory

Otterhoofd

I'm reading an article (http://prb.aps.org/abstract/PRB/v82/i4/e045122) but I have some problems understanding certain definitions. The authors have introduced a basis of certain bands (four) and then continue to give the transformation matrices of the symmetry operators. One (rotation) of them is given as:
[tex]R2=\sigma_1 \otimes\tau_3[\tex]
with "In the above, sigma acts in the spin basis and tau acts in the basis of P1+ and P2− subbands"

What does this product look like? Is it really a kronecker/direct product of the two matrices? I'm confused because they work in different bases. Or can I just do the kronecker product, resulting in i times:
0 0 1 0
0 0 0 -1
1 0 0 0
0 -1 0 0

In the appendix, gamma matrices are also defined in a similar way.

Can anyone point me in the right direction or give some insight on this? Thanks