We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: \[ \begin{cases} \partial_{t}u(t,φ)+\mathcal{L}u(t,φ)+f(t,φ,u(t,φ),\partial_{x}u(t,φ) σ(t,φ),(u(\cdot,φ))_{t})=0,\;t\in[0,T),\;φ\in\mathbbΛ\, ,u(T,φ)=h(φ),\;φ\in\mathbbΛ, \end{cases} \] where $\mathbbΛ=\mathcal{C}([0,T];\mathbb{R}^{d})$, $(u(\cdot ,φ))_{t}:=(u(t+θ,φ))_{θ\in[-δ,0]}$ and \[ \mathcal{L}u(t,φ):=\langle b(t,φ),\partial_{x}u(t,φ)\rangle+\dfrac {1}{2}\mathrm{Tr}\big[σ(t,φ)σ^{\ast}(t,φ)\partial_{xx} ^{2}u(t,φ)\big]. \] The result is obtained by a stochastic approach. In particular we prove a new type of nonlinear Feynman-Kac representation formula associated to a backward stochastic differential equation with time-delayed generator which is of non-Markovian type. Applications to the large investor problem and risk measures via $g$-expectations are also provided.