Pseudodifferential operators on filtered manifolds as generalized fixed points

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct pseudodifferential extension that reflects behaviour. corresponding calculus, principal symbol an operator is family operators acting on certain nilpotent Lie groups. The role ellipticity as Fredholm condition replaced by Rockland these Our approach allows understand in terms representations algebra symbols. Moreover, compute K-theory algebra.