Compositio Math. 117 (1999), pp. 47-81.
I explained the results of 1999a and 1999b in my talk at the conference for Oort's 60th birthday in 1995. I'm not sure why they took so long to be published, except that at some point one of the journals lost the manuscript.

Erratum

The claim at the end of the introduction: "In a later article (Milne, 1999b), I shall use Theorem 7.1 to construct a canonical category of "motives" over $\mathbb{F}$…" was too optimistic. At the time I wrote it, I thought that the left hand square at the bottom of p65 together with Theorem 6.1, i.e., $P=L\cap S$ (inside $T$) would (by the theory of tannakian categories) allow you to complete the right hand square. This is obviously true if the tannakian categories were neutral with fibre functors that match, but the question with nonneutral categories is much more subtle. Roughly speaking, one wants to define $\mathrm{Mot}(\mathbb{F}{})$ to be the "quotient" of $\mathrm{LMot}(\mathbb{F}% )\otimes\mathrm{CM}(\mathbb{Q}^{\mathrm{al}})$ by $\mathrm{LCM}(\mathbb{Q}{}^{\mathrm{al}})$. Cf. my article Quotients of Tannakian Categories.

In 1.7, $\mathbb{T}=h(\mathrm{Spec}(k),\mathrm{id},1)$ (the $h$ is missing).

From Sjoerd de Vries:
You use a filtration of $\mathbb{Q}^{\mathrm{cm}}$ (the union of all CM subfields of $\mathbb{Q}^{\mathrm{al}}$) by CM subfields to prove your results. At some point, you need to assume that these are "sufficiently large"; in particular, you want the decomposition group in your proofs to have size at least 3. You make some assumptions on page 22 of the paper, under the heading "Completion of the proof of the Theorem 6.1", but these are not enough. There are counterexamples when $K = \mathbb{Q}(i,\sqrt{n})$ for suitable choices of $n$ (depending on $p$). See also paragraph 4.4.1 in my masters thesis,* and the proof of Lemma 4.4.8 in particular. I suppose the point is that $d-1 = 1$ if $d=2$.

It suffices to add the condition that $K$ contains a degree $> 2$ real subfield in which $p$ is inert.

*Available at Notes.