FORT LAUDERDALE, Fla. — Vanishing profits from new-car sales. A slumping U.S. market. The future of auto retailing in doubt as the promise of mobility and autonomous vehicles takes grip.

Where does this leave the head of the largest U.S. dealership group?

"I feel like the Cheshire cat," Mike Jackson, CEO of AutoNation Inc., said from his headquarters here last week, a day after he wrapped up a three-week tour of the U.S., where he met with managers and department heads from each of his 274 dealerships.

"A period of significant, disruptive change is coming. I made my move years ago, and I like the way it's going to play out."

Jackson, 68, was referring to steps that began almost five years ago, when he decided to paste the AutoNation name across all of his stores except those that sell luxury cars. That initiative was extended late last year, when he outlined a vision for AutoNation auctions, used-car outlets and collision centers and branded parts, accessories and finance and insurance products.

And he topped it off this month, when he announced an agreement to provide service to Waymo's self-driving vehicles.

"I like the fact that we're in the entire spectrum," Jackson said. "Now where this famous line moves between personal use and sharing, I'm in the game on both sides."

As Jackson, starting his 19th year as AutoNation's chief executive, sees it, he has one foot anchored in the future while using the scale of his $21.61 billion enterprise to control his path in the traditional world of selling and servicing privately owned vehicles.

And contrary to some pundits, he believes that world still has plenty of life.

So with a new duo of top lieutenants — Lance Iserman, 52, sales boss and COO, and Scott Arnold, 59, executive vice president of customer care — Jackson crystallized the brand-extension strategy.