You’ve got to hand it to Jeff Tweedy: He keeps doing his thing, with no apparent regard for what radio programmers or the rest of us think about it.

His band, Wilco — perhaps America’s most critically scrutinized rock combo — returns to the Murat on Friday for its third U.S. date on a world tour that has spent the past month in Europe. The effort supports the new release, Sky Blue Sky, Wilco’s sixth studio album, and the first for the current six-man lineup seen on recent Indiana visits and the 2005 live album, Kicking Television.

Joining guitarist-vocalist-songwriter Tweedy are bassist John Stirratt (the only other remnant of the original quartet), percussionist Glenn Kotche, keyboardist Mikael Jorgensen and multi-instrumentalist Pat Sansone. The band’s secret weapon is its newest member, Nels Cline, a ridiculously skilled lead guitarist who is equally fluent with smooth jazz runs, Lou Reed-style bursts of angry distortion and the lonesome whine of the lap steel.

Sky Blue Sky continues in the direction Wilco has taken since troubled guitar-keyboard-studio whiz Jay Bennett was booted six years ago. The vibe ranges from SoCal singer-songwriter to R&B to prog rock, but the artsy deconstructions and winking historical references are less common. Oddly, as the band keeps adding members and textures, the arrangements grow more cohesive and focused on serving Tweedy’s beautiful melodies and increasingly direct lyrics. Sky Blue Sky has warmth that reflects the live, ambient recording style the band has honed in its Chicago home studio, dubbed The Loft.

The down side is that they sometimes forget to bring the rock, and the album lapses into a cloying prettiness. Concertgoers should hope for the band to let loose a bit on stage and include a few chestnuts from the A.M. and Being There era of the mid ’90s.

But those concerns probably don’t matter much to the guy who wrote Sky Blue Sky’s “What Light,” an archetypal folk song that seems to blow in from Dylan territory: And if you’re trying to paint a picture / And you’re not sure which colors belong / Just paint what you see / Don’t let anyone say it’s wrong.