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The alt-Latin rock group Cafe Tacuba wouldn’t seem to be big on anniversaries. Its lead singer goes by a series of nicknames, the quartet often favors chicken-head and lucha libre masks, and its name comes from a Mexico City coffee shop.

So you might not expect the Tacubans to go the conventional route and celebrate an anniversary. But true to its antic spirit, the band is celebrating with a twist: two milestones, the 20th anniversary of its landmark album “Re” and the 25th anniversary of the group itself on the “20re-ct25 Tour,” which stops Oct. 22 at the Portage Theater in Chicago and which will feature the band performing the album in its entirety.

Cafe Tacuba might be iconoclastic, says Enrique “Quique” Rangel, the group’s co-founder, bassist and occasional vocalist, but not so completely nonconformist that it doesn’t appreciate a significant anniversary. “I don’t think the band decides whether we’re celebrating another year — or just taking another step on the ladder. We don’t know where this ladder is going to lead us, but our fans demand that we make something special for them.”

Then again, “Re” is not just any album. The 20-track release features many of the band’s signature songs, such as “La Ingrata,” “El Ciclon,” “Esa Noche” and “Las Flores.”

In 2012, Rolling Stone magazine put “Re” in the No. 1 spot on its list of the 10 Greatest Latin Rock Albums of All Time, proclaiming “Every album that the Mexican quartet released after this one is just as good but ‘Re’ defined the rules of the game.”

It also redefined the career trajectory of Cafe Tacuba. “‘Re’ opened a lot of doors for us, not only in Mexico, but in South America and the United States,” Rangel said. “The songs from ‘Re’ have remained in our concert repertoire all these years. When people pick one song to describe our music, they usually choose something from ‘Re.’ Our fans have really embraced this album to the point that we feel these songs no longer belong just to us. We think these songs belong to the people, and that’s why we decided to make this tour.”

In Chicago, Cafe Tacuba often plays the much larger Aragon, but on this tour, it will appear at the Portage Theater, a vintage movie palace that reopened in June as a mixed-use venue. “I have worked with Cafe Tacuba before,” said Charlie Burns, the Portage’s new operator. “I have a personal and working relationship with the band and its production team.”

And on the alt-Latin scene, no band has a higher profile than Cafe Tacuba — a status that has prompted some lofty comparisons. “Re” has been called Mexico’s answer to the Beatles’ so-called White Album, a description that amuses Rangel. “Some people in Mexico find that kind of thing insulting,” he said, laughing. “For us, the fact that we are four, and we have experimented in a wide spectrum of genres, it is easy to say, ‘This is the Mexican Beatles.’ It is an honor that people think in those terms, but we are not them. Besides, you have bad luck when you try to imitate the Beatles.”

Though many fans might think the album’s title refers to the Latin “re” (“in the manner of” or English shorthand for “regarding”), Rangel said it’s a Spanish prefix, often used to mean “once again” or more colloquially in Mexico, “twisting” or “twisted.” “For us, it came to stand for ‘revolution’ or ‘revelation.’ In that period, we were trying to figure out our (artistic) purpose. The lyrics of ‘El Ciclon’ talk about going ’round and ’round until you get to the same place. That represents one of the main themes of ‘Re.'”

On the album, Cafe Tacuba throws virtually every traditional Mexican style — norteno, ranchera, bolero, son — into its alt-Latin mix, layered over a foundation of guitar rock, punk, ska, metal and more. “We were developing as musicians, and we were aiming our ambitions very high,” he said. “Our abilities were not on the same (plane) but we were determined to find an original voice from this place called Mexico.”

Guiding the band on this journey was Gustavo Santaolalla, perhaps the most influential producer on the Latin rock scene then and now. He produced Cafe Tacuba’s first album in 1992 and went on to produce the rest of the band’s catalog, save for one disc. “We had so many songs for ‘Re,’ and we thought that he would tell us that it would be too much,” Rangel said. “But he told us if we wanted to record 20 songs, they had to be the best. If that was our creative goal, he was there to help us realize our vision. Back then, we were still discovering how to use the studio as a tool, and he helped us put our vision on the tracks.”

Though “Re” is now hailed as a masterpiece, the album initially “didn’t sell that well,” he said. “Over the years, people became much more aware of the album and appreciative. Not that it changed my mind. It was a good record from the start. In time, it came to have the place we thought it deserved. And now we are revisiting that. I feel proud.”

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When: 8 p.m. Oct. 22

Where: Portage Theater, 4050 N. Milwaukee Ave.

Tickets: $33, $38; 773-283-7244 or portagetheater.com