  Axion insulators are generally understood as magnetic topological insulators
whose Chern-Simons axion coupling term is quantized and equal to $\pi$.
Inversion and time reversal, or the composition of either one with a rotation
or a translation, are symmetries which protect this invariant. In this work, we
focus our attention on the composition of a 2-fold rotation with time reversal,
and we show that insulators with this symmetry possess a Z2 invariant arising
from Atiyah's real K-theory. We call this invariant the K-theory Kane-Mele
invariant due to the similarities it has with the Kane-Mele invariant for
systems with time-reversal symmetry. Whenever all Chern numbers vanish, we
demonstrate that this invariant is equivalent to the Chern-Simons axion
coupling, and in the presence of the inversion symmetry, we show how this
invariant could be obtained from the eigenvalues of the inversion operator on
its fixed points in momentum space. For the general case of non-trivial Chern
numbers, the Chern-Simons axion coupling term incorporates information of the
K-theory Kane-Mele invariant as well as information regarding bands with
non-trival Chern numbers. An explicit formula in terms of K-theory generators
is presented for the Chern-Simons axion coupling term, the relation with the
K-theory Kane-Mele invariant is explained, and a formula in terms of
eigenvalues of the inversion operator is obtained. Using an effective
Hamiltonian model and first-principles calculations, we also show that the
occurrence of bulk-band inversion and nontrivial K-theory Kane-Mele invariant
index can be observed in axion insulators of the pnictides family. In
particular, we demonstrate that NpBi can be classified as an axion insulator
due to the detection of additional topological indicators such as the quantum
spin Hall effect, gapped surface states, surface quantized anomalous Hall
effect, and chiral hinge modes
