In explicitly correlated Moller-Plesset (MP2-R12) methods, the first-order wave function is expanded not only in terms of products of one-electron functions-that is, orbitals-but also in terms of two-electron functions that depend linearly on the interelectronic coordinates r(ij). With these functions, three-and four-electron integrals occur, but these integrals can be avoided by inserting a resolution of the identity (RI) in terms of the one-electron basis. In previous work, only one single basis was used for both the electronic wave function and the RI approximation. In the present work, a new computational approach is developed that uses an auxiliary basis set to represent the RI. This auxiliary basis makes it possible to employ standard basis sets in explicitly correlated MP2-R12 calculations.