  Let K be an algebraically closed field, X a K-scheme, and X(K) the set of
closed points in X. A constructible set C in X(K) is a finite union of subsets
Y(K) for finite type subschemes Y in X. A constructible function f : X(K) --> Q
has f(X(K)) finite and f^{-1}(c) constructible for all nonzero c. Write CF(X)
for the Q-vector space of constructible functions on X.
  Let phi : X --> Y and psi : Y --> Z be morphisms of C-varieties. MacPherson
defined a Q-linear "pushforward" CF(phi) : CF(X) --> CF(Y) by "integration"
w.r.t. the topological Euler characteristic. It is functorial, that is, CF(psi
o phi)=CF(psi) o CF(phi). This was extended to K of characteristic zero by
Kennedy.
  This paper generalizes these results to K-schemes and Artin K-stacks with
affine stabilizers. We define notions of Euler characteristic for constructible
sets in K-schemes and K-stacks, and pushforwards and pullbacks of constructible
functions, with functorial behaviour. Pushforwards and pullbacks commute in
Cartesian squares. We also define "pseudomorphisms", a generalization of
morphisms well suited to constructible functions problems.
