Homotopy Theoretic Study of Higher Dimensional Categories

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I tried to make a new construction of algebraic K-theory based on formal group laws of general heights, e.g., Honda group law. Formal group laws other than additive or multiplicative group, do not give algebraic groups, but can be regarded as a gamma set defined by Segal. Since a gamma set is a simplicial set, we have a homotopy type by taking the geometric realization. We consider the full matrix algebra over a ring of integers of a local field. Then the resulting homotopy type is a candidate for a space of algebraic K-theory of higher height. First I studied the cohomology group of the space. In the case of multiplicative group, the space is the classifying space of the general linear group. The cohomology is symmetric polynomials of the cohomology of the maximal torus. If the height of the formal group law is h, then the dimension of the maximal torus is h-times of the ordinary case. Then we obtain a multi-symmetric polynomials as cohomology of the space for the candidate. What we have to do next is to define or construct the representation theory based on a given formal group law of higher height. In particular I hope to get a group theoretic interpretation of Hokins-Kuhn-Ravenel character not using the Morava K-theory.