Unfortunately, foreign individuals cannot own a property in Indonesia. All property, land or buildings, have to be registered in the name of an Indonesian citizen.
There are options to control freehold land via a corporate structure, a PMA (international company) if the company is domiciled and operating in Indonesia. There are, however, many restrictions, obligations and complications, which make this option unattractive for private individuals to invest in Indonesia.
The easiest way to control property is via a leasehold of land and building for a given period (generally 25 years with options to extend). The transaction is usually formalised via a public notary and fully recognised by Indonesian law.
By obtaining a lease contract, the lessee becomes the effective owner of that property for the period of the lease with all obligations and privileges that come with the property. The lessee has the right to sell the lease and include the asset in a will.