I'm asking this question in the context of the current Supreme Court case McCoy v. Louisiana in which the fundamental issue is whether it is unconstitutional for defense counsel to concede an accused's guilt over the accused's express objection.

I didn't quite understand this quote from the respondent's brief:

This Court has held that a few important rights—“to plead guilty, waive a jury, testify in his or her own behalf, or take an appeal”—may be waived only with the client’s consent. Jones, 463 U.S. at 751. But “[w]ith the exception of these specified fundamental decisions, an attorney’s duty is to take professional responsibility for the conduct of the case, after consulting with his client.” Jones, 463 U.S. at 753 n.6. In Florida v. Nixon, 543 U.S. 175 (2004), the Court declined to add contesting guilt at the guilt phase of a capital trial to that list. Nixon concluded that strategically conceding guilt in a capital case is not “the equivalent of a guilty plea” and may be defense counsel’s wisest course. Id. at 189- 191. As the Court explained, a “guilty plea is ‘more than a confession which admits that the accused did various acts,’ it is a ‘stipulation that no proof by the prosecution need be advanced.’” Id. at 188 (quoting Boykin v. Alabama, 395 U.S. 238, 242 (1969)). A “plea is not simply a strategic choice; it is itself a 31 conviction.” Id. at 187 (citation and internal quotation marks omitted).