MINNEAPOLIS—For thousands of Minnesotans mourning the death of George Floyd, the corner of East 38th Street and Chicago Avenue in Minneapolis has grown over the past few days from a gritty commercial district and busy thruway to the city’s emotional center.

Tucked near the intersection is Cup Foods, the small, family-run grocery store that Mr. Floyd visited before being arrested by police on May 25. The memorial site started as a small pile of balloons and flowers. But over the past week, it has swelled into a block-wide gathering…

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