We study higher order corrections to the radius/M2-brane charge of AdS_4 x
S^7/Z_k. There are two sources of corrections: one from the orbifold
singularity of C^4/Z_k, and the other from the discrete torsion associated with
the homology 3-cycle H_3(S^7/Z_k,Z) = Z_k. We give a precise formula for the
charge shift. These corrections are relevant, for example, at two loops in the
AdS_4 x CP^3 sigma model, and therefore for the strong coupling test of the all
loop Bethe ansatz.Comment: 16 pages; v2: The Type IIA D-brane probe calculation has been
corrected, and now agrees with the M theory calculation. Appendix on
conventions for RR fields and D-brane actions added. Note added on a possible
correction due to a parity anomaly. References adde
