The Adidas team was huddled with Kanye West, pitching ideas for the first shoe they would create together. It was 2013, and the rapper and the sportswear brand had just agreed to become partners. The Adidas employees, thrilled to get started, had arrayed sneakers and fabric swatches on a long table near a mood board pinned with images.

But nothing they showed that day at the company’s German headquarters captured the vision Mr. West had shared. To convey how offensive he considered the designs, he grabbed a sketch of a shoe and took a marker to the toe, according to two participants. Then he drew a swastika.

It was shocking, especially to the Germans in the group. Most displays of the symbol are banned in their country. The image was acutely sensitive for a company whose founder belonged to the Nazi Party. And they were meeting just miles from Nuremberg, where leaders of the Third Reich were tried for crimes against humanity.

That encounter was a sign of what was to come during a collaboration that would break the boundaries of celebrity endorsement deals. Sales of the shoes, Yeezys, would surpass $1 billion a year, lifting Adidas’s bottom line and recapturing its cool. Mr. West, who now goes by Ye, would become a billionaire.

When the company ended the relationship last October, it appeared to be the culmination of weeks of Mr. West’s inflammatory public remarks — targeting Jews and disparaging Black Lives Matter — and outside pressure on the brand to cut ties. But it was also the culmination of a decade of Adidas’s tolerance behind the scenes.

Inside their partnership, the artist made antisemitic and sexually offensive comments, displayed erratic behavior, and issued ever escalating demands, a New York Times examination found. Adidas’s leaders, eager for the profits, time and again abided his misconduct.

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