Tap dancer/choreographer Michelle Dorrance can improvise and kick it old school with the best of them. But as she and her spirited New York-based company showed Friday night at Arlington’s Regent Theatre, the Bessie Award-winner has made her most groundbreaking contribution to the evolution of tap through tight, polished choreographic numbers that put the genre to the service of theatrical context. Drawing inspiration from music ranging from the Squirrel Nut Zippers and Fiona Apple to The Bluegrass Reunion and Big Maybelle, she crafts dances with personality, precision and charming touches of clever, sometimes daffy humor. She and her dancers, 14 in all for Friday’s show, dress in a variety of mostly colorful street wear, and they don’t just show off prodigious technical feats, they become a community of characters who hint at engaging narratives.