  We apply an idea of framed vertex operator algebras to a construction of
local conformal nets of (injective type III_1) factors on the circle
corresponding to various lattice vertex operator algebras and their twisted
orbifolds. In particular, we give a local conformal net corresponding to the
moonshine vertex operator algebras of Frenkel-Lepowsky-Meurman. Its central
charge is 24, it has a trivial representation theory in the sense that the
vacuum sector is the only irreducible DHR sector, its vacuum character is the
modular invariant J-function and its automorphism group (the gauge group) is
the Monster group. We use our previous tools such as alpha-induction and
complete rationality to study extensions of local conformal nets.
