Let $R$ be a connective (symmetric) ring spectrum. Let $GL_1(R)$ be the space of units of $R$, i.e. the union of the components of $\Omega^{\infty}(R)$ corresponding to the units of $\pi_0(R)$. $GL_1(R)$ is a group-like monoid, therefore it makes sense to speak about $BGL_1(R)$.

In fact, if $R$ is a commutative spectrum, then $GL_1(R)$ has the structure of an infinite loop space and defines a spectrum $gl_1(R)$.

Are there any sensible methods to analyze $BGL_1(R)$ in the non-commutative case?

As an example of what I mean, let me mention that $BGL_1(R)$ maps to $K(R)$ the algebraic $K$-theory of the ring spectrum $R$, which in turn maps to $THH(R)$ - the topological Hochschild homology. Thus, information about $THH(R)$ might tell you something about $BGL_1(R)$.