Hecke algebra of an algebraic group

Definition
Let $$G$$ be an algebraic group over a field $$k$$ and $$B$$ be a Borel subgroup of $$G$$. The Hecke algebra of $$G$$ (corresponding to $$B$$) over a commutative unital ring $$R$$ is defined as the defining ingredient::centralizer ring for $$B$$ in $$G$$ with respect to $$R$$.

Note that $$R$$ need not be equal to the field $$k$$.