MAP is a solution to $L(\theta) = \mathcal{I}[\theta \ne \theta^{*}]$

Question

I have come across these slides in one of the online courses. The instructor was trying to explain how Maximum Posterior Estimate(MAP) is actually the solution $L(\theta) = \mathcal{I}[\theta \ne \theta^{*}]$, where $\theta^{*}$ is the true parameter.

Can someone please explain how this follows?