We consider the extension of classical 2-dimensional topological quantum
field theories to Klein topological quantum field theories which allow
unorientable surfaces. We approach this using the theory of modular operads by
introducing a new operad governing associative algebras with involution. This
operad is Koszul and we identify the dual dg operad governing A-infinity
algebras with involution in terms of Mobius graphs which are a generalisation
of ribbon graphs.