Is  there  a  comprehensive  account  of  GEOMETRIC equivariant spin  bordism  groups  with  respect  to  the  group $ \mathbb{Z}/2$ (instead  of  homotopy theoretical trough equivariant Thom Spectra), which  allow  actions  which are  not  free?.  I  am interested  only  in  low  dimensions  0  to  6. 
 
There  is  a  computation of  the  free bordism groups done  by  Gianvalbo (1976,  conference  proceedings of  transformation  groups conference  in newcastle  upon Tyne), Using  KO Pontrjagyn classes  and  the  splitting  method from  Anderson-Brown-Peterson  to  determine the  free bordism  groups by  making  the  trick  of  computing  $\Omega_n^{\rm Spin}(B \mathbb{Z}/2)$. However,  this  computation is  seriously  flawed,  producing  groups   with  a  higher  rank  as  possible, as  one  can  easily   check  with  the  Atiyah-Hirzebruch  Spectral sequence.