In this note we will illustrate a method for computing the $\pi_0$ of the effective log motive of a smooth and proper variety over a perfect field $k$ and show that it is $\mathbf{ A}^1$-invariant. We will apply this to compute the first homotopy groups of $\mathbf{ P}^1$ to show that the stripping functor from log motivic sheaves to (usual) Nisnevich sheaves with transfers is fully faithful.
Categories: math.AG