= Algebraic quotient by a finite group
{title2=$X/G=\operatorname{Spec}(A^G)$}
For an <affine variety> with <coordinate ring> $A$ acted on by a <finite group> $G$, the affine quotient is $\operatorname{Spec}A^G$. Elements of $A$ satisfy monic orbit polynomials over $A^G$, so the quotient map is a <finite morphism>. Over an <algebraically closed field>, invariant functions separate finite orbits; in characteristic not dividing $|G|$, interpolate and average a function separating two orbits. The quotient fibres are consequently the orbits.
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