  In this paper, we construct proper pushforwards and flat pullbacks in Chow
groups of coherent sheaf stacks over a Deligne-Mumford(DM) stack.
  When there is a relative semi-perfect obstruction theory for a DM-type
morphism $X \to Y$, $X$ is a DM stack and $Y$ is a DM stack or a smooth Artin
stack, we define a virtual pull-back as a bivariant class. This is an analogue
of virtual pull-backs defined by Manolache.
