Non-equivariantly, symplectic bordism has  been  developed  extensively  by  Ray, Gorbunov, and  specially  S. Kochman in this memoir: http://dx.doi.org/10.1090/memo/0496 Yet  the  coefficients  remain  unknown  outside  of  the  range reached  by  Kochman.  

Is  there  any development  of  equivariant symplectic  bordism?