When you have a cognitive disability, you spend much of your life waiting to be invited. And when you finally are, in Kelly Hunter’s words, it often goes something like this:

“Oh, please come over for a visit. And bring your elder son. But for God’s sake, don’t bring the younger one because he’s autistic, and that will be too much stress for everyone.”

People on the autism spectrum. People who have had brain injuries or strokes. People with mental illness. People at any stage of dementia. People who are nonverbal. They have a standing invitation to stay home.

Hunter’s groundbreaking staging of “Pericles,” now touring Colorado in partnership with Denver’s disability-affirmative Phamaly Theatre Company, welcomes them all.

And they don’t just park their wheelchairs in a corner, dim the lights and forget about them for 90 minutes as they go about performing the play. Instead, they put them in the action as fully participating members of the acting company — reciting lines, playing characters. Fully engaged.

They are so welcome here, in fact, they are greeted by Phamaly company members who sing the word “Hello,” followed by their actual names, as they enter the building. That, Hunter said, is meant to ease their anxiety as they transition into an unfamiliar setting: this theater.

“For our visitors, I believe the experience starts the minute you walk into the theater space,” said Hunter, visiting artistic director of London’s Flute Theatre. It is a simple welcoming rite that is repeated again and again for 20 minutes.

“We welcome our autistic audience by creating an existential, womblike space,” she said. “The heartbeat is the first sound you hear in the womb before you are born, and the heartbeat is at the center of Shakespeare’s verse.

“We are giving an autistic person who might otherwise live entirely within a 24-7 panic attack the best chance for their body and their interior rhythm to be calmer and more relaxed than they would normally be in a public space.”

This thinking is grounded in decades of scientific research about how to make an autistic person not only feel safe in an unfamiliar environment but to help them come fully alive. The greeting at the door is just the beginning of what soon plays out as a seductive, ritualistic experience. There will be chanting, there will be repetition. There will be music and dance and game-playing. There will be silly faces and goo-goo eyes. There will be undeniable human connection. There will be smiles that light up a room that is kept otherwise intentionally dark to prevent overstimulation. There will even be a play, sort of.

This utterly unique experience invites up to 12 people with cognitive disabilities to sign up in advance and fully participate in the storytelling. Those who do are each partnered with two professional Phamaly Theatre Company actors who act as caretakers by safely guiding them through every step of telling Shakespeare’s story, and their important parts in it.

“And those 12 people are likely to have a life-changing experience because they are the center of the performance,” said Hunter, who has been working with a variety of marginalized communities for 25 years.

Inside the actual theater — last weekend, that was The Loft Theatre on the campus of the University of Colorado in Boulder; this weekend it will shift to the Ent Center for the Arts in Colorado Springs — you must imagine a circle in a square. The participating visitors and their guides first form a circle that essentially constitutes the playing area. The rest of us — a cross-section of parents, friends and fascinated general theatergoers, — take our seats behind them in a single row of chairs that forms a square around them.

How does this turn into an effective telling of Shakespeare’s problematic swashbuckler? You get the bones of the story, Hunter says — or at least the bones that Hunter thinks are most skeletal to this particular audience.

“You’ll still see everything that matters,” said Hunter, herself once an actor with the prestigious Royal Shakespeare Company. “We follow the story of a man who has to flee for his life until he meets a down-to-earth fisherman who tells him there’s a beautiful girl down the road who’s about to get married. But she doesn’t love him, so — go get her.”

There are very few line exchanges in Hunter’s production. But every triad of performers gets a chance to play each one three times or more – their confidence and understanding growing each time.

The play ends as it began, with the professional Phamaly actors gently preparing their guests to transition out of this welcoming world they have created and back to their not-always-welcoming outside lives. By now, their loved ones have joined them on stage. A massive dance party breaks out. The joy is palatable, and palpable. For all of them.

“As the years have gone on, I’ve realized that what I have created is doubly worth the effort for the families and the caregivers than it is even for the autistic person themselves,” Hunter said. “Because, think about what life is like for them. From the age of 2 or thereabouts, your loved child who you would die for has been deemed a problem. Something is wrong. And they are laughed at and spat at and pointed at. And even if you know intellectually that it’s not your fault, you’re going to think it’s your fault because human beings do that to themselves. So the guilt, the shame, the anxiety, the wishing life was different — even for the best people with the best attitude — that is always there.

“And this experience reverses that. So we flipped what was a problem into a source of absolute pleasure.”