  Motivated by the theory of bi-singular pseudodifferential operators, we
introduce a two dimensional version of the Adler-Manin trace. Our construction
is rather general in the sense that it involves a twist afforded by an algebra
automorphism. That is, starting from an algebra equipped with an automorphism,
two twisted derivations, and a twisted invariant trace, we construct an algebra
of formal twisted pseudodifferential symbols and define a noncommutative
residue. Also, we provide related examples.
