The partner’s plan, McKinsey noted, was to “respect traditional bureaucratic process including use of bribes.” McKinsey also wrote that the partner had identified eight “key Indian officials” — named in the PowerPoint slide — whose influence was needed for the deal to go through. Nowhere in the slide did McKinsey advise that such a scheme would be illegal or unwise.

McKinsey declined to provide The New York Times with its full report or any evidence that it had objected to the paying of bribes. But the consultancy denied recommending “bribery or other illegal acts.” For his part, the Ukrainian oligarch, Dmitry V. Firtash, denies that he paid or recommended bribes, or had any dealings with McKinsey or knowledge of the document.

The story of McKinsey’s role in the episode has remained hidden from public view for 12 years. Even today the firm’s ultimate recommendation and how its client, Boeing, responded remain something of a mystery, cloaked in the secrecy of grand jury proceedings. But McKinsey’s reference to illegal acts has thrust the firm into a tangled international battle over the extradition of Mr. Firtash, who has been charged in the United States with bribing Indian officials in anticipation of getting titanium for Boeing.

Should he be brought to trial, McKinsey, and the document it produced, stand to play a major role in the outcome — a well of potential embarrassment that underscores the risks that McKinsey and other American consulting firms face as they, and clients like Boeing, do business in countries where ethical standards and practices diverge from those at home.

McKinsey initially refused to confirm that the report even existed. But after learning that The Times had obtained a copy, the firm issued a statement acknowledging that McKinsey employees had indeed written it. Neither McKinsey nor Boeing agreed to an interview.