  We relate the group structure of van der Kallen on orbit sets of unimodular
rows with values in a smooth algebra $A$ over a field $k$ with the motivic
cohomotopy groups of the spectrum of $A$ with coefficients in
$\mathbb{A}^n\setminus 0$ in the sense of Asok and Fasel. In the last section,
we compare the motivic cohomotopy theory studied in this paper and defined by
$\mathbb{A}^{n+1}\setminus 0$ or, equivalently, by an $\mathbb{A}^1$-weakly
equivalent quadric $Q_{2n+1}$ to that considered by Asok and Fasel, defined by
a quadric $Q_{2n}$, by means of explicit morphisms $Q_{2n+1}\rightarrow
Q_{2n}$, $Q_{2n}\times\mathbb{G}_m\rightarrow Q_{2n+1}$ of quadrics.
