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Let $R$ be a reduced real affine algebra of dimension $d \ge 2$ such thateither $R$ has no real maximal ideals, or the intersection of all real maximalideals in $R$ has a height of at least one. In this article, we prove thefollowing: (1) the $d$-th Euler class group $\text{E}^d(R)$ is canonicallyisomorphic to the Chow group $\text{CH}_0(\text{Spec}(R))$ of zero cycles on$\text{Spec}(R)$ modulo rational equivalence; (2) the universal Mennicke symbol$\text{MS}_{d+1}(R)$ is canonically isomorphic to the universal weak Mennickesymbol $\text{WMS}_{d+1}(R)$; and (3) additionally if $R$ is a smooth variety,then the Whitehead group $\mathrm{SK_1}(R)$ is canonically isomorphic to$\frac{\text{SL}_{d+1}(R)}{\text{E}_{d+1}(R)}$.

Zero cycles, Mennicke symbols and $\mathrm{K}_1$-stability of some real affine algebras