I had to implement the projection preconditioner (P = I - A*R*(A_H)^1 *P) along with an standard preconditioner (M).

And I read in some thread of users list that multilevel preconditioner can better handled by PCMG too, thus 

I had tried to implement the later (M) as pre smoother, where as the earlier (P) as CGC in PCMG framework.

1. Does it make sense ?
or the coarse grid correction of PCMG only does this part: R*(A_H)^1 *P   ??
2. How can I adapt my projection preconditioner (P) as (P1 = I - A*R*(A_H)^1 *P + R*(A_H)^1 *P ) ?