Convergence of two obstructions for projective modules

Let $X=SpecA$ denote a regular affine scheme, over a field $k$, with $1\mathrm{/}2\in k$ and $\dim X=d$. Let $P$ denote a projective $A$-module of rank $n\ge 2$. Let ${\pi }_0(\mathcal{L}O(P))$ denote the (Nori) Homotopy Obstruction set, and ${\widetilde{CH}}^n(X,{\mathrm{\Lambda }}^{n}P)$ denote the Chow Witt group. In this article, we define a natural (set theoretic) map} $${\mathrm{\Theta }}_P:{\pi }_0(\mathcal{L}O(P))⟶{\widetilde{CH}}^n(X,{\mathrm{\Lambda }}^{n}P)$$ The main Results are included in my recently published book on Algebraic $K$-Theory.