A tenant rents commercial property and invests substantial capital to renovate and improve the space in order to run a business. Does the renter's investment entitle them to equity or a percentage of ownership in the property?
Normally a tenant doesn't build equity.
Normally when a tenant makes modifications to the rental property, the modifications if they can't be removed, are now owned by the landlord. It is possible to negotiate a credit of some sort so that if a tenant has to make modifications they don't end up paying for all the costs. I have seen this where company renting office space was given a budget to refresh the paint, and carpet, or two move some walls. Of course the owner calculated this budget when determining the amount of rent.
It is best to negotiate these deals long before committing to the modifications. It lets you know the costs, and what can be saved at the end of the rental period. It also lets you know if you will have to pay to put things back at the end of the lease.
No, there is no entitlement to equity or a percentage of ownership in the property unless explicitly agreed to between landlord and tenant.
That would be an extremely odd ask from a tenant. A tenant might be able negotiate a lower rent or other concessions if they are making capital investments that the landlord can benefit from beyond the lease term. But with commercial leases commonly being 5-10 years, it's perfectly normal for the tenant to expend their own capital with no concessions to customize a space to their liking. In fact, a tenant might have to spend money to return the space to how they found it if customized too much.
With that information, it's prudent for the tenant to shop around for a space that they don't have to customize as much upfront. If a business requires a highly customized space in order to operate regardless (like a manufacturing facility), then the business should consider owning the space since it's more of an inherent part of operating the business.