In algebraic geometry, the Chow group of a stack is a generalization of the Chow group of a variety or scheme to stacks. For a quotient stack X = [ Y / G ] {\displaystyle X=[Y/G]} , the Chow group of X is the same as the G-equivariant Chow group of Y. A key difference from the theory of Chow groups of a variety is that a cycle is allowed to carry non-trivial automorphisms and consequently intersection-theoretic operations must take this into account.
In algebraic geometry, the Chow group of a stack is a generalization of the Chow group of a variety or scheme to stacks. For a quotient stack X = [ Y / G ] {\displaystyle X=[Y/G]} , the Chow group of X is the same as the G-equivariant Chow group of Y. A key difference from the theory of Chow groups of a variety is that a cycle is allowed to carry non-trivial automorphisms and consequently intersection-theoretic operations must take this into account.
Source: Wikipedia "Chow group of a stack" · CC BY-SA 4.0
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