  In this paper, we study the multiplicity and concentration of the positive
solutions to the following critical Kirchhoff type problem: \begin{equation*}
  -\left(\varepsilon^2 a+\varepsilon b\int_{\R^3}|\nabla u|^2\mathrm{d}
x\right)\Delta u + V(x) u = f(u)+u^5\ \ {\rm in } \ \ \R^3, \end{equation*}
where $\varepsilon$ is a small positive parameter, $a$, $b$ are positive
constants, $V \in C(\mathbb{R}^3)$ is a positive potential, $f \in C^1(\R^+,
\R)$ is a subcritical nonlinear term, $u^5$ is a pure critical nonlinearity.
When $\varepsilon>0$ small, we establish the relationship between the number of
positive solutions and the profile of the potential $V$. The exponential decay
at infinity of the solution is also obtained. In particular, we show that each
solution concentrates around a local strict minima of $V$ as $\varepsilon
\rightarrow 0$.
