We propose a method to construct the virtual fundamental class based on the
"Kontsevich principle," i.e., we formulate the notion of quasi manifold st
ructrue and establish a way to obtain the fundamental class from it. Also,
we show that there is a natural quasi manifold structure on the moduli stac
k of stable maps, and thus we arrive at the new construction of the Gromov-
Witten class. We also prove the fixed point formula for our Gromov-Witten c
lass.