One of the most memorable Shakespeare productions I have ever seen was a remarkable Othello staged in the vecindades of Mexico City in 1988 by theatre-makers Arturo Ramírez and Martín López Cruz. Vecindades are the oldest and most common form of housing in my country – perhaps inspired by Aztec homes, they're communal buildings with a main entrance leading to a wide central courtyard surrounded by the front doors of each individual residence.

The theatre company travelled from courtyard to courtyard presenting the story of a man – the Othello character – whose appointment as the administrator of a residential block enrages another tenant, who bitterly believes himself worthy of the position, causing him to engineer the moral destruction of the good man. It was performed in modern dress in these communal courtyards, and real residents freely came and went as if they were part of the action. I remember the last scene being incredible: during a party that culminated with Othello's final outburst, the actors would knock on the doors and entice the neighbours out to dance. As Desdemona died, the courtyard resonated strangely with the rhythms of an infectious danzón.

In my country, there is no writer more popular, or whose plays have been staged more often in the last 10 years. At this very moment, in fact, there are two versions of The Tempest running in Mexico City. A few weeks ago, a monologue version of Macbeth finished its run, as well as a Merchant of Venice with three actors; less that a year ago, the Compañía Nacional de Teatro commissioned a police force-influenced Romeo and Juliet, and not too long ago the Universidad Nacional dedicated its primary theatrical season to the staging of three different versions of Othello.

Shakespeare is Mexican, I think, because he speaks our language, and by that I don't just mean Spanish, but the language spoken in the furthest margins of the country: not so long ago, in an effort to confront issues within their community, a rural school performed a workshop production of Romeo and Juliet in Purépecha, a small district in the highlands of the north-west. Although fewer than 100,000 people speak it, I'd vouch that Purépecha is one of the most melodious languages there is – and when married to Shakespeare's rich verse, it proved almost unbearably poignant.

Perhaps it might seem strange for people used to hearing or reading him in English, but despite the fact that Mexico is mentioned by Shakespeare only once – in The Merchant of Venice, if I'm not mistaken – we hear and see so much Shakespeare that I would wager that ser o no ser rings truer than "to be or not to be". He truly is Mexican.

• Luis Mario Moncada is the writer of A Soldier in Every Son: The Rise of the Aztecs, inspired by Shakespeare's history plays, which is currently showing as part of the World Shakespeare festival