  For a number field, we have a Tannaka category of mixed Tate motives at our
disposal. We construct p-adic points of the associated Tannaka group by using
p-adic Hodge theory. Extensions of two Tate objects yield functions on the
Tannaka group, and we show that evaluation at our p-adic points is essentially
given by the inverse of the Bloch-Kato exponential map.
