nLab Lefschetz motive

There exists a motive $\mathbf{L}$, called the Lefschetz motive, such that the motive of the projective line decomposes as

$$h(\mathbf{P}^1_k) = h(\Spec(k)) \oplus \mathbf{L}$$

Formally inverting the Lefschetz motive in the category of effective pure motives yields the category of pure motives.