If you’re a New York City resident and attend the theater at least occasionally, chances are you’ve been to a production where the performance is preceded by an announcement acknowledging the indigenous people who once owned the land beneath the venue. Now, the playwright Mary Kathryn Nagle, a citizen of the Cherokee Nation, has made their harrowing history the subject of “Manahatta.”

The title of Ms. Nagle’s play references how Manhattan was identified by members of the Lenape tribes who inhabited it before losing it to Dutch colonists in the 17th century, in a deal that has been subject to scholarly debate but that clearly involved swindling. For this play, Ms. Nagle — who is also an attorney focused on the rights of Indian nations and “the restoration of tribal sovereignty,” according to her playbill bio — draws both on this injustice and a more recent example of exploitation fueled by greed.

The protagonist of “Manahatta” boasts an impressive resume as well, though her ambitions have led her to a rather less altruistic pursuit. Jane Snake, born to Lenape parents in Oklahoma — one of a few states their ancestors settled in after having been driven from their homes — is a Stanford Business School graduate who was also valedictorian of her class at MIT.

When we meet Jane, she’s interviewing for a position at a hot-shot Manhattan investment bank, eventually disclosed to be Lehman Brothers. It’s 2002, meaning that firm is six years away from imploding in our century’s first and, thus far, worst financial crisis. In fact, Ms. Nagle’s own law firm was involved in litigation suing banks implicated in that catastrophe, which ultimately proved far less devastating for the big banks than the less affluent Americans who had been sold on the myth that their salvation lay in subprime mortgage loans.   

Jane’s family seems destined to a similar fate after her father dies, leaving her mother in deep debt, thanks in part to the outrageously priced surgery that failed to save his life. Shifting between the early years of the 21st century and the 1600s, Ms. Nagle tries to forge a connection between the Lenape men, women, and children who were tricked and then driven out — or worse — by Dutch colonists and today’s Native American citizens, who suffer both racial and economic oppression.

It’s an intriguing premise, and director Laurie Woolery brings undeniable theatrical flair to the production, in which actors cast in dual roles shift between characters with increasing fluidity as the distant and recent past are documented in ever closer proximity, and eventually collide. Unfortunately, the exercise is hampered by Ms. Nagle’s sometimes reductive character portraits and clunky, cliché-ridden dialogue.

“Everyone loves money,” the slick, impatient Lehman exec who hires Jane  intones after chiding her for taking the subway to the interview. (He helicopters into work, apparently.) “To succeed at this job, you need something else. Something more.” In the next scene, having returned to Oklahoma for her father’s funeral, Jane gets flak from her resentful sister, Deb, who sneers, “I guess they don’t teach you to use common sense in grad school.”

Deb is soon forced to move in with their mother, as the latter struggles not to lose her home. A local banker who has been a longtime friend tries to help out, and seems well-meaning at first: A white man, he’s the adopted father of the indigenous Luke, Jane’s old pal, who clearly still carries a torch for her — though Luke becomes frustrated as his buddy, rising through the ranks at Lehman, grows increasingly disconnected from her family.

Mind you, neither Luke nor anyone else bothers to tell Jane, until it’s too late, about the increasingly dire situation her mother is facing — one she could easily resolve in the five seconds it takes to sign a check in the middle five figures. Ms. Nagle is more interested in stoking moral arguments; when Luke, working for his father, warns Jane that her accomplishments “won’t open the door for me” or “anyone else from our community,” she declares, “I’d rather be the exception than a failure.” 

The 17th-century characters can prove equally caricature-like, particularly those drawn from history. Jeffrey King is tasked with playing both the Dutch colonial governor who orchestrated the purchase of Manhattan, Peter Minuit, and Lehman’s CEO, Dick Fuld, and it’s hard to say which emerges as the more cartoonish villain. As Se-ket-tu-may-qua, or “Black Beaver” — named for a Lenape tribal leader who actually lived in the 1800s — Enrico Nassi, who also plays Luke quite endearingly, is pretty much relegated to the role of noble protector, warning women about the dangers of Dutch men. 

Elizabeth Frances, cast as both Jane and Se-ket-tu-may-qua’s partner, Le-le-wa’-you, joins Mr. Nassi — who prowls silently behind the 21st-century characters at various points — in most obviously straddling the different eras and the not unrelated challenges they pose. But while Jane’s inner conflict is certainly not ignored, neither is it fleshed out or made dramatically compelling.

That’s a shame, because the concerns addressed in “Manahatta” are profound and enduring, and Ms. Nagle’s perspective would seem as uniquely informed as it is vital. More stories like these must be told, however flawed the execution in this case.